Rfast reference manual
Μιχαήλ Τσαγρής
Ioannis Tsamardinosvisibility
…
description
281 pages
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1 file
A collection of fast and very fast R functions written in R or C++.
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Package ‘Rfast’
March 10, 2018
Type Package
Title A Collection of Efficient and Extremely Fast R Functions
Version 1.8.8
Date 2018-03-10
Author Manos Papadakis, Michail Tsagris, Marios Dimitriadis, Stefanos Fafalios, Ioannis Tsamardinos, Matteo Fasiolo, Giorgos Borboudakis, John Burkardt, Changliang Zou and Kleanthi Lakiotaki
Maintainer Manos Papadakis <papadakm95@gmail.com>
Depends R (>= 3.2.2), Rcpp (>= 0.12.3), RcppZiggurat
LinkingTo Rcpp (>= 0.12.3), RcppArmadillo
SystemRequirements C++11
URL https://rfast.eu
Description A collection of fast (utility) functions for data analysis. Column- and rowwise means, medians, variances, minimums, maximums, many t, F and Gsquare tests, many regressions (normal, logistic, Poisson), are some of the many fast functions.
License GPL (>= 2.0)
LazyData TRUE
NeedsCompilation yes
Repository CRAN
Date/Publication 2018-03-10 22:49:03 UTC
R topics documented:
Rfast-package . . . . . . . . . . . . . . . . . . . .
All k possible combinations from n elements . . . .
Analysis of covariance . . . . . . . . . . . . . . .
Analysis of variance with a count variable . . . . .
Angular central Gaussian random values simulation
ANOVA for two quasi Poisson regression models .
Backward selection regression . . . . . . . . . . .
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R topics documented:
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BIC (using partial correlation) forward regression . . . . . .
BIC forward regression with generalised linear models . . .
Binary search algorithm . . . . . . . . . . . . . . . . . . . .
Binomial coefficient and its logarithm . . . . . . . . . . . .
Bootstrap t-test for 2 independent samples . . . . . . . . . .
Check if any column or row is fill with zeros . . . . . . . . .
Check if values are integers and convert to integer . . . . . .
Check Namespace and Rd files . . . . . . . . . . . . . . . .
Check whether a square matrix is symmetric . . . . . . . . .
Cholesky decomposition of a square matrix . . . . . . . . .
Circular or angular regression . . . . . . . . . . . . . . . .
Circular-linear correlation . . . . . . . . . . . . . . . . . . .
Column and row wise coefficients of variation . . . . . . . .
Column and row-wise Any/All . . . . . . . . . . . . . . . .
Column and row-wise means of a matrix . . . . . . . . . . .
Column and row-wise medians . . . . . . . . . . . . . . . .
Column and row-wise nth smallest value of a matrix/vector .
Column and row-wise Order - Sort Indices . . . . . . . . . .
Column and row-wise products . . . . . . . . . . . . . . . .
Column and row-wise range of values of a matrix . . . . . .
Column and row-wise ranks . . . . . . . . . . . . . . . . .
Column and row-wise Shuffle . . . . . . . . . . . . . . . .
Column and row-wise sums of a matrix . . . . . . . . . . .
Column and row-wise tabulate . . . . . . . . . . . . . . . .
Column and row-wise variances and standard deviations . .
Column and rows-wise mean absolute deviations . . . . . .
Column-row wise minima and maxima of two matrices . . .
Column-wise differences . . . . . . . . . . . . . . . . . . .
Column-wise kurtosis and skewness coefficients . . . . . . .
Column-wise matching coefficients . . . . . . . . . . . . . .
Column-wise minimum and maximum . . . . . . . . . . . .
Column-wise MLE of some univariate distributions . . . . .
Column-wise true/false value . . . . . . . . . . . . . . . . .
Column-wise uniformity Watson test for circular data . . . .
Column-wise Yule’s Y (coefficient of colligation) . . . . . .
Correlation based forward regression . . . . . . . . . . . . .
Correlation between pairs of variables . . . . . . . . . . . .
Correlations . . . . . . . . . . . . . . . . . . . . . . . . . .
Covariance and correlation matrix . . . . . . . . . . . . . .
Cox confidence interval for the ratio of two Poisson variables
Cross-Validation for the k-NN algorithm . . . . . . . . . . .
data.frame.to_matrix . . . . . . . . . . . . . . . . . . . . .
Density of the multivariate normal and t distributions . . . .
Design Matrix . . . . . . . . . . . . . . . . . . . . . . . . .
Diagonal Matrix . . . . . . . . . . . . . . . . . . . . . . . .
Distance between vectors and a matrix . . . . . . . . . . . .
Distance correlation . . . . . . . . . . . . . . . . . . . . . .
Distance matrix . . . . . . . . . . . . . . . . . . . . . . . .
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R topics documented:
Distance variance and covariance . . . . . . . . . . . . . . . . . . . . . . . . . .
Eigenvalues and eigenvectors in high dimensional principal component analysis .
Energy distance between matrices . . . . . . . . . . . . . . . . . . . . . . . . .
Equality of objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Estimation of an AR(1) model . . . . . . . . . . . . . . . . . . . . . . . . . . .
Estimation of the Box-Cox transformation . . . . . . . . . . . . . . . . . . . . .
Exponential empirical likelihood for a one sample mean vector hypothesis testing
Exponential empirical likelihood hypothesis testing for two mean vectors . . . .
FBED variable selection method using the correlation . . . . . . . . . . . . . . .
Find element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Find the given value in a hash table . . . . . . . . . . . . . . . . . . . . . . . . .
Fitted probabilities of the Terry-Bradley model . . . . . . . . . . . . . . . . . .
Fitting a Dirichlet distribution via Newton-Rapshon . . . . . . . . . . . . . . . .
Floyd-Warshall algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Forward selection with generalised linear regression models . . . . . . . . . . .
G-square test of conditional indepdence . . . . . . . . . . . . . . . . . . . . . .
Gaussian regression with a log-link . . . . . . . . . . . . . . . . . . . . . . . . .
Generates random values from a normal and puts them in a matrix . . . . . . . .
Get specific columns/rows fo a matrix . . . . . . . . . . . . . . . . . . . . . . .
Hash - Pair function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hash object to a list object . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
High dimensional MCD based detection of outliers . . . . . . . . . . . . . . . .
Hypothesis test for the distance correlation . . . . . . . . . . . . . . . . . . . . .
Hypothesis test for two means of percentages . . . . . . . . . . . . . . . . . . .
Hypothesis test for von Mises-Fisher distribution over Kent distribution . . . . .
Hypothesis testing betseen two skewness or kurtosis coefficients . . . . . . . . .
Index of the columns of a data.frame which are factor variables . . . . . . . . . .
Insert new function names in the NAMESPACE file . . . . . . . . . . . . . . . .
Inverse of a symmetric positive definite matrix . . . . . . . . . . . . . . . . . . .
James multivariate version of the t-test . . . . . . . . . . . . . . . . . . . . . . .
k nearest neighbours algorithm (k-NN) . . . . . . . . . . . . . . . . . . . . . . .
k-NN algorithm using the arc cosinus distance . . . . . . . . . . . . . . . . . . .
Linear models for large scale data . . . . . . . . . . . . . . . . . . . . . . . . .
Logistic and Poisson regression models . . . . . . . . . . . . . . . . . . . . . .
Logistic or Poisson regression with a single categorical predictor . . . . . . . . .
Lower and Upper triangular of a matrix . . . . . . . . . . . . . . . . . . . . . .
Mahalanobis distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many (and one) area aunder the curve values . . . . . . . . . . . . . . . . . . .
Many 2 sample proportions tests . . . . . . . . . . . . . . . . . . . . . . . . . .
Many 2 sample tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many analysis of variance tests with a discrete variable . . . . . . . . . . . . . .
Many ANCOVAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many exponential regressions . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many F-tests with really huge matrices . . . . . . . . . . . . . . . . . . . . . . .
Many G-square tests of indepedence . . . . . . . . . . . . . . . . . . . . . . . .
Many Gini coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many hypothesis tests for two means of percentages . . . . . . . . . . . . . . . .
Many moment and maximum likelihood estimations of variance components . .
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R topics documented:
Many multi-sample tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many multivariate simple linear regressions coefficients . . . . . . . . . . . . . . .
Many non parametric multi-sample tests . . . . . . . . . . . . . . . . . . . . . . .
Many odds ratio tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many one sample goodness of fit tests for categorical data . . . . . . . . . . . . .
Many one sample tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many random intercepts LMMs for balanced data with a single identical covariate.
Many regression based tests for single sample repeated measures . . . . . . . . . .
Many score based GLM regressions . . . . . . . . . . . . . . . . . . . . . . . . .
Many score based regression models . . . . . . . . . . . . . . . . . . . . . . . . .
Many Shapiro-Francia normality tests . . . . . . . . . . . . . . . . . . . . . . . .
Many simple circular or angular regressions . . . . . . . . . . . . . . . . . . . . .
Many simple Gaussian regressions with a log-link . . . . . . . . . . . . . . . . . .
Many simple geometric regressions . . . . . . . . . . . . . . . . . . . . . . . . .
Many simple linear mixed model regressions . . . . . . . . . . . . . . . . . . . .
Many simple linear regressions coefficients . . . . . . . . . . . . . . . . . . . . .
Many simple multinomial regressions . . . . . . . . . . . . . . . . . . . . . . . .
Many tests for the dispersion parameter in Poisson distribution . . . . . . . . . . .
Many two-way ANOVAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Many univariate generalised linear models . . . . . . . . . . . . . . . . . . . . . .
Many univariate simple binary logistic regressions . . . . . . . . . . . . . . . . . .
Many univariate simple linear regressions . . . . . . . . . . . . . . . . . . . . . .
Many univariate simple poisson regressions . . . . . . . . . . . . . . . . . . . . .
Many univariate simple quasi poisson regressions . . . . . . . . . . . . . . . . . .
Many Welch’s F-tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Match . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrix with all pairs of t-tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrix with G-square tests of indepedence . . . . . . . . . . . . . . . . . . . . . .
Mean - Median absolute deviation of a vector . . . . . . . . . . . . . . . . . . . .
Median of a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minima and maxima of two vectors/matrices . . . . . . . . . . . . . . . . . . . . .
minimum and maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
minimum and maximum frequencies . . . . . . . . . . . . . . . . . . . . . . . . .
MLE for multivariate discrete data . . . . . . . . . . . . . . . . . . . . . . . . . .
MLE of (hyper-)spherical distributions . . . . . . . . . . . . . . . . . . . . . . . .
MLE of continuous univariate distributions defined on the positive line . . . . . . .
MLE of continuous univariate distributions defined on the real line . . . . . . . . .
MLE of count data (univariate discrete distributions) . . . . . . . . . . . . . . . .
MLE of distributions defined in the (0, 1) interval . . . . . . . . . . . . . . . . . .
MLE of some circular distributions . . . . . . . . . . . . . . . . . . . . . . . . . .
MLE of the inverted Dirichlet distribution . . . . . . . . . . . . . . . . . . . . . .
MLE of the multivariate normal distribution . . . . . . . . . . . . . . . . . . . . .
MLE of the ordinal model without covariates . . . . . . . . . . . . . . . . . . . .
MLE of the tobit model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Moment and maximum likelihood estimation of variance components . . . . . . .
Multi-sample tests for vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multinomial regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multivariate kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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R topics documented:
Multivariate Laplace random values simulation . . . . . . . . . . . . . . . . . . . . . .
Multivariate normal and t random values simulation . . . . . . . . . . . . . . . . . . . .
Naive Bayes classifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Natural Logarithm each element of a matrix . . . . . . . . . . . . . . . . . . . . . . . .
Natural logarithm of the beta function . . . . . . . . . . . . . . . . . . . . . . . . . . .
Natural logarithm of the gamma function and its derivatives . . . . . . . . . . . . . . . .
Norm of a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Number of equal columns between two matrices . . . . . . . . . . . . . . . . . . . . . .
Odds ratio and relative risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
One sample empirical and exponential empirical likelihood test . . . . . . . . . . . . . .
One sample t-test for a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Operations between two matrices or matrix and vector . . . . . . . . . . . . . . . . . .
Orthogonal matching pursuit regression . . . . . . . . . . . . . . . . . . . . . . . . . .
Permutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Permutation based p-value for the Pearson correlation coefficient . . . . . . . . . . . . .
Prediction with some naive Bayes classifiers . . . . . . . . . . . . . . . . . . . . . . . .
Quasi binomial regression for proportions . . . . . . . . . . . . . . . . . . . . . . . . .
Quasi Poisson regression for count data . . . . . . . . . . . . . . . . . . . . . . . . . .
Random intercepts linear mixed models . . . . . . . . . . . . . . . . . . . . . . . . . .
Random values simulation from a von Mises distribution . . . . . . . . . . . . . . . . .
Ranks of the values of a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reading the files of a directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Repeated measures anova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Replicate columns/rows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Round each element of a matrix/vector . . . . . . . . . . . . . . . . . . . . . . . . . . .
Row - Wise matrix/vector count the frequency of a value . . . . . . . . . . . . . . . . .
Row-wise minimum and maximum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Row-wise true value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Search for variables with zero range in a matrix . . . . . . . . . . . . . . . . . . . . . .
Significance testing for the coefficients of Quasi binomial or the quasi Poisson regression
Simulation of random values from a Bingham distribution . . . . . . . . . . . . . . . .
Simulation of random values from a Bingham distribution with any symmetric matrix . .
Simulation of random values from a normal distribution . . . . . . . . . . . . . . . . . .
Simulation of random values from a von Mises-Fisher distribution . . . . . . . . . . . .
Skeleton of the PC algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Skewness and kurtosis coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Some summary statistics of a vector for each level of a grouping variable . . . . . . . . .
Sort - Sort a vector coresponding to another . . . . . . . . . . . . . . . . . . . . . . . .
Sort and unique numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sorting of the columns-rows of a matrix . . . . . . . . . . . . . . . . . . . . . . . . . .
Source many R files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spatial median for Euclidean data . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spherical and hyperspherical median . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Standardisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sub-matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sum of a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sum of all pairwise distances in a distance matrix . . . . . . . . . . . . . . . . . . . . .
Sums of a vector for each level of a grouping variable . . . . . . . . . . . . . . . . . . .
5
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6
Rfast-package
Table Creation - Frequency of each value . . . . . . . .
Tests for the dispersion parameter in Poisson distribution
Topological sort of a DAG . . . . . . . . . . . . . . . .
Transpose of a matrix . . . . . . . . . . . . . . . . . . .
Two sample exponential empirical likelihood test . . . .
Uniformity test for circular data . . . . . . . . . . . . .
Variance of a vector . . . . . . . . . . . . . . . . . . . .
Vector allocation in a symmetric matrix . . . . . . . . .
Weibull regression model . . . . . . . . . . . . . . . . .
Yule’s Y (coefficient of colligation) . . . . . . . . . . . .
Index
Rfast-package
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Really fast R functions
Description
A collection of Rfast functions for data analysis. Note 1: The vast majority of the functions accept
matrices only, not data.frames. Note 2: Do not have matrices or vectors with have missing data
(i.e NAs). We do no check about them and C++ internally transforms them into zeros (0), so you
may get wrong results. Note 3: In general, make sure you give the correct input, in order to get the
correct output. We do no checks and this is one of the many reasons we are fast.
Details
Package:
Type:
Version:
Date:
License:
Rfast
Package
1.8.8
2018-03-10
GPL-2
Maintainers
Manos Papadakis <papadakm95@gmail.com>
Note
Acknowledgments:
We would like to acknowledge Professor Kurt Hornik, Doctor Uwe Ligges (and the rest of R core
team) for their invaluable help with this R package. Erich Studerus for his invaluable comments
and Neal Fultz for his suggestions. Vassilis Vasdekis for his invaluable help with the random effects
models. Marios Dimitriadis work was funded by the Special Account for Research Funds of the
University of Crete, Department of Computer Science. Phillip Si is greatly acknowledged for his
All k possible combinations from n elements
7
help with the Floyd-Warshal algorithm. Keefe Murphy for his invaluable help with NEWS file and
for his suggestions. Zacharias Papadovassilakis gave us the inspiration for the memory efficient
version of the k-NN algorithm. Yannis Pantazis explained us how the orhtogonal matching pursuit
works. Achim Zeileis for his help with the quasi Poisson regression models. Pedro J. Aphalo for
finding a bug. Dimitris Yannikis for finding a bug. Acknowledgements to Christina Chatzipantsiou
for her idea with the "permcor" and the "boot.ttest2" functions.
Author(s)
Manos Papadakis <papadakm95@gmail.com>, Michail Tsagris <mtsagris@yahoo.gr>, Marios Dimitriadis <kmdimitriadis@gmail.com>, Stefanos Fafalios <stefanosfafalios@gmail.com>, Ioannis
Tsamardinos <tsamard@csd.uoc.gr>, Matteo Fasiolo <matteo.fasiolo@gmail.com>, Giorgos Borboudakis <borbudak@gmail.com>, John Burkardt <jburkardt@fsu.edu> and Kleanthi Lakiotaki
<kliolak@gmail.com>
All k possible combinations from n elements
All k possible combinations from n elements
Description
All k possible combinations from n elements.
Usage
comb_n(n, k)
Arguments
n
A positive or negative INTEGER number or a vector with numbers.
k
A positive integer number at most equal to n or at most equal to the length of n,
if n is a vector.
Value
A matrix with k columns and rows equal to the number of possible unique combinations of n with
k elements.
Author(s)
Manos Papadakis and Marios Dimitriadis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com> and Marios
Dimitriadis <kmdimitriadis@gmail.com>.
References
Nijenhuis A. and Wilf H.S. (1978). Combinatorial Algorithms for Computers and Calculators.
Academic Press, NY.
8
Analysis of covariance
See Also
nth, colMaxs, colMins, colrange
Examples
system.time( comb_n(20, 4) )
system.time( combn(20, 4) )
x <- rnorm(5)
comb_n(x, 3)
Analysis of covariance
Analysis of covariance
Description
Analysis of covariance
Usage
ancova1(y, ina, x, logged = FALSE)
Arguments
y
A numerical vector with the data, the response variable.
ina
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Be
careful, the function is desinged to accept numbers greater than zero.
x
A numerical vector whose length is equal to the number of rows of y. This is the
covariate.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
Analysis of covariance is performed. No interaction between the factor and the covariate is tested.
Only the main effects. The design need not be balanced. The values of ina need not have the same
frequency. The sums of squares have been adjusted to accept balanced and unbalanced designs.
Value
A matrix with the test statistic and the p-value for the factor variable and the covariate.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Analysis of variance with a count variable
9
References
D.C. Montgomery (2001). Design and analysis of experiments (5th Edition). New York: John
Wiley \& Sons
See Also
ancovas, ftests, ttests, anova1
Examples
y <- rnorm(90)
ina <- rbinom(90, 2, 0.5) + 1
x <- rnorm(90)
system.time( a <- ancova1(y, ina, x) )
m1 <- lm(y ~ factor(ina) + x)
m2 <- lm(y ~ x + factor(ina))
anova(m1)
anova(m2)
Analysis of variance with a count variable
Analysis of variance with a count variable
Description
Analysis of variance with a count variable.
Usage
poisson.anova(y, ina, logged = FALSE)
geom.anova(y, ina, type = 1, logged = FALSE)
quasipoisson.anova(y, ina, logged = FALSE)
Arguments
y
A numerical vector with discrete valued data, i.e. counts.
ina
A numerical vector with discrete numbers starting from 1, i.e. 1, 2, 3, 4,... or
a factor variable. This is suppose to be a categorical predictor. If you supply a
continuous valued vector the function will obviously provide wrong results.
type
This argument is for the geometric distribution. Type 1 refers to the case where
the minimum is zero and type 2 for the case of the minimum being 1.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
10
Angular central Gaussian random values simulation
Details
This is the analysis of variance with Poisson or geometric distributed data. What we do is a loglikelihood ratio test. However, this is exactly the same as Poisson regression with a single predictor
variable who happens to be categorical. Needless to say that this is faster function than the glm command in R. For the same purpose with a Bernoulli variable use g2Test. The quasinpoisson.anova
is when in the glm function you specify family = quasipoisson. This is suitable for the case of over
or under-dispersed data.
Value
A vector with two values, the difference in the deviances (or the scale difference in the case of
quasi poisson) and the relevant p-value. The quasipoisson.anova also returns the estimate of the φ
parameter.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
logistic.cat1, g2Test, poisson.anovas, anova, poisson_only,poisson.mle
Examples
y <- rpois(300, 10)
ina <- rbinom(300, 3, 0.5) + 1
a1 <- poisson.anova(y, ina)
a2 <- glm(y ~ ina, poisson)
a1
anova(a2, test = "Chisq")
y <- rgeom(300, 0.7)
geom.anova(y, ina)
Angular central Gaussian random values simulation
Angular central Gaussian random values simulation
Description
Angular central Gaussian random values simulation.
Usage
racg(n, sigma)
ANOVA for two quasi Poisson regression models
11
Arguments
n
The sample size, a numerical value.
sigma
The covariance matrix in Rd .
Details
The algorithm uses univariate normal random values and transforms them to multivariate via a
spectral decomposition. The vectors are then scaled to have unit length.
Value
A matrix with the simulated data.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Tyler D. E. (1987). Statistical analysis for the angular central Gaussian distribution on the sphere.
Biometrika 74(3): 579-589.
See Also
acg.mle, rmvnorm, rmvlaplace, rmvt
Examples
s <- cov( iris[, 1:4] )
x <- racg(100, s)
acg.mle(x)
vmf.mle(x) ## the concentration parameter, kappa, is very low, close to zero, as expected.
ANOVA for two quasi Poisson regression models
ANOVA for two quasi Poisson regression models
Description
ANOVA for two quasi Poisson regression models.
Usage
anova_quasipois.reg(mod0, mod1, n)
12
ANOVA for two quasi Poisson regression models
Arguments
mod0
An object as returned by the "qpois.reg" function. This is the null model.
mod1
An object as returned by the "qpois.reg" function. This is the alternative model.
n
The sample size. This is necessary to calculate the degrees of freedom.
Details
This is an ANOVA type significance testing for two quasi Poisson models.
Value
A vector with 4 elements, the test statistic value, its associated p-value and the relevant degrees of
freedom of the numerator and the denominator.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Papke L. E. & Wooldridge J. (1996). Econometric methods for fractional response variables with an
application to 401(K) plan participation rates. Journal of Applied Econometrics, 11(6): 619–632.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
anova_qpois.reg, qpois.reg, univglms, quasipoisson.anova
Examples
y <- rnbinom(200, 10, 0.5)
x <- matrix(rnorm(200 * 3), ncol = 3)
a1 <- qpois.reg(x, y)
a0 <- qpois.reg(x[, 1], y)
anova_quasipois.reg(a0, a1, 200)
b1 <- glm(y ~ x, family = quasipoisson)
b0 <- glm(y ~ x[, 1], family = quasipoisson)
anova(b0, b1, test = "F")
c1 <- glm(y ~ x, family = poisson)
c0 <- glm(y ~ x[, 1], family = poisson)
anova(c0, c1, test = "Chisq")
Backward selection regression
13
Backward selection regression
Backward selection regression
Description
Backward selection regression.
Usage
bs.reg(y, x, alpha = 0.05, type = "logistic")
Arguments
y
A numerical vector with the response variable values. It can either be of 0 and 1
values (Logistic regression) or of integer values 0, 1, 2,... (Poisson regression).
x
A numerical matrix with the candidate variables.
alpha
Threshold (suitable values are in [0,1]) for assessing the significance of p-values.
The default value is at 0.05.
type
For the Logistic regression put "logistic" (default value) and for Poisson type
"poisson".
Details
This function currently implements only the binary Logistic and Poisson regressions. If the sample size is less than the number of variables a notification message will appear and no backward
regression will be performed.
Value
The output of the algorithm is an S3 object including:
info
A matrix with the non selected variables and their latest test statistics and pvalues.
Vars
A vector with the selected variables.
Author(s)
Marios Dimitriadis
R implementation and documentation: Marios Dimitriadis <mtsagris@csd.uoc.gr>
See Also
fs.reg, univglms, cor.fsreg
14
BIC (using partial correlation) forward regression
Examples
y <- rbinom(50, 1, 0.5)
x <- matrnorm(50, 10)
bs.reg(y, x)
BIC (using partial correlation) forward regression
BIC (using partial correlation) forward regression
Description
BIC (using partial correlation) forward regression.
Usage
bic.corfsreg(y, x, tol = 2)
Arguments
y
A numerical vector.
x
A matrix with data, the predictor variables.
tol
If the BIC difference between two successive models is less than the tolerance
value, the variable will not enter the model.
Details
The forward regression tries one by one the variables using the F-test, basically partial F-test every
time for the latest variable. This is the same as testing the significance of the coefficient of this latest
enetered variable. Alternatively the correlation can be used and this case the partial correlation
coefficient. There is a direct relationship between the t-test statistic and the partial correlation
coefficient. Now, instead of having to calculate the test statistic, we calculate the partial correlation
coefficient. The largest partial correlation indicates the candidate variable to enter the model. If the
BIC of the regression model with that variable included, reduces, less than "tol" from the previous
model without this variable, the variable enters.
Value
A matrix with two columns, the index of the selected variable(s) and the BIC of each model. The
first line is always 0 and the BIC of the model with no predictor variables.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
BIC forward regression with generalised linear models
15
References
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
See Also
cor.fsreg, score.glms, univglms, logistic_only,poisson_only, regression
Examples
## 200 variables, hence 200 univariate regressions are to be fitted
x <- matrix( rnorm(200 * 200), ncol = 200 )
y <- rnorm(200)
system.time( a1 <- bic.corfsreg(y, x) )
system.time( a2 <- cor.fsreg(y, x) )
x <- NULL
BIC forward regression with generalised linear models
BIC forward regression with generalised linear models
Description
BIC forward regression with generalised linear models.
Usage
bic.fs.reg(y, x, tol = 2, type = "logistic")
Arguments
y
A numerical vector.
x
A matrix with data, the predictor variables.
tol
If the BIC difference between two successive models is less than the tolerance
value, the variable will not enter the model.
type
If you have a binary dependent variable, put "logistic". If you have count data,
put "poisson".
Details
The forward regression tries one by one the variables using the BIC at each step for the latest
variable. If the BIC of the regression model with that variable included, is less than "tol" from the
previous model without this variable, the variable enters.
Value
A matrix with two columns, the index of the selected variable(s) and the BIC of each model.
16
Binary search algorithm
Author(s)
Marios Dimitriadis
R implementation and documentation: Marios Dimitriadis <kmdimitriadis@gmail.com>.
References
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
See Also
fs.reg, bic.corfsreg, cor.fsreg, score.glms, univglms, logistic_only,poisson_only, regression
Examples
## 200 variables, hence 200 univariate regressions are to be fitted
x <- matrix(rnorm(200 * 200), ncol = 200)
y <- rbinom(200, 1, 0.5)
a <- bic.fs.reg(y, x)
x <- NULL
Binary search algorithm
Binary search algorithm
Description
Search a value in an ordered vector.
Usage
binary_search(x, v, index=FALSE)
Arguments
x
A vector with the data.
v
A value to check if exists in the vector x.
index
A boolean value for choose to return the position inside the vector.
Details
The functions is written in C++ in order to be as fast as possible.
Value
Search if the v exists in x. Then returns TRUE/FALSE if the value is been found.
Binomial coefficient and its logarithm
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
is_element
Examples
x <- sort(rnorm(1000))
v <- x[50]
b <- binary_search(x,v)
b1 <- binary_search(x,v,TRUE)
Binomial coefficient and its logarithm
Binomial coefficient and its logarithm
Description
Binomial coefficient and its logarithm.
Usage
Lchoose(x, k)
Choose(x, k)
Arguments
x
A vector with integer values numbers.
k
A positive non zero at most equal to x.
Details
The binomial coefficient or its logarithm are evaluated.
Value
A vector with the answers.
Author(s)
Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
17
18
Bootstrap t-test for 2 independent samples
See Also
comb_n, Lbeta, Lgamma
Examples
x <- sample(20:30, 100, replace = TRUE)
Choose(x, 4)
Lchoose(x, 4)
x<-NULL
Bootstrap t-test for 2 independent samples
Bootstrap t-test for 2 independent samples
Description
Bootstrap t-test for 2 independent samples.
Usage
boot.ttest2(x, y, B = 999)
Arguments
x
A numerical vector with the data.
y
A numerical vector with the data.
B
The number of bootstrap samples to use.
Details
Instead of sampling B times from each sample, we sample sqrtB from each of them and then take
all pairs. Each bootstrap sample is independent of each other, hence there is no violation of the
theory.
Value
A vector with the test statistic and the bootstrap p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>.
Check if any column or row is fill with zeros
19
References
B.L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika,
38(3/4), 330-336.
Efron Bradley and Robert J. Tibshirani (1993). An introduction to the bootstrap. New York: Chapman \& Hall/CRC.
See Also
ttest2, ftest
Examples
tic <- proc.time()
x <- rexp(40, 4)
y <- rbeta(50, 2.5, 7.5)
system.time( a <- boot.ttest2(x, y, 9999) )
a
Check if any column or row is fill with zeros
Check if any column or row is fill with zeros
Description
Check if any column or row is fill with zeros.
Usage
colrow.zero(x)
Arguments
x
A vector with data.
Details
Check all the column if any has all its elements zeros. If found, return "TRUE". Otherwise continues
with rows. If columns and rows hasn’t any zero vector then return "FALSE". Even if it returns
"FALSE" that doesn’t mean the determinant can’t be zero. It might be but if check before and
found any zero vector then for sure the determinant it’ll be zero.
Value
A boolean value, "TRUE" if any column OR row is zero. "FALSE" otherwise.
20
Check if values are integers and convert to integer
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, rowFalse, nth, colrange, colMedians, colVars, sort_mat, rowTrue
Examples
x <- matrix(runif(10*10),10,10)
colrow.zero(x)
x<-NULL
Check if values are integers and convert to integer
Check if values are integers and convert to integer
Description
Check if values are integers and convert to integer.
Usage
is_integer(x)
as_integer(x,result.sort = TRUE,init = 1)
Arguments
x
is_integer: A vector with numeric data. as_integer: A vector with data.
result.sort
A logical value for sorting the result.
init
An integer value to start.
Details
The behavior of these functions are different than R’s built in.
is_integer: check if all the values are integers in memory. If typeof is double, and the values are
integers in range -2^31 : 2^31 then it is better to convert to integer vector for using less memory.
Also you can decrease the time complexity.
as_integer: converts the discrete values to integers.
Check Namespace and Rd files
21
Value
is_integer: A logical value, TRUE if all values are integers and in range -2^31 : 2^31. Otherwise
FALSE.
as_integer: By default the function will return the same result with "as.numeric" but the user can
change the "init" value not start from 1 like R’s. Also the result can be unsorted using "result.sort".
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
as_integer, colVars, colmeans, read.directory
Examples
x<-runif(10)
y1<-is_integer(x) # y1 is FALSE
x<-as.numeric(rpois(10,10)) # integers but typeof is double
y1<-is_integer(x) # y1 is TRUE so you can convert to integer vector.
as_integer(letters) ## as.numeric(letters) produce errors
x<-y1<-NULL
Check Namespace and Rd files
Check Namespace and Rd files
Description
Check Namespace/Rd and examples files.
Usage
checkNamespace(path.namespace,path.rfolder)
checkAliases(path.man,path.rfolder,dont.read = "")
checkTF(path.man,dont.read = "")
checkExamples(path.man,each = 1,dont.read = "",print.errors = stderr(),
print.names = FALSE)
Arguments
path.namespace An full path to the "NAMESPACE" file.
path.rfolder
An full path to the directory that contains the "R" files.
path.man
An full path to the directory that contains the "Rd" files.
each
An integer value for running each example.
22
Check Namespace and Rd files
dont.read
A character vector with the name of the files that you wish not to read. By
default it’s empty "".
print.errors
Print the errors to a file. By default it’s "stdeer()".
print.names
A boolean value (TRUE/FALSE) for printing the names of the files before running the examples.
Details
For function "checkNamespace": reads from the NAMESPACE folder all the export R functions,
reads from folder R all the R functions and check if all the functions are export.
For function "checkAliases": reads from the man directory all the Rd files, then reads from each
file the aliases and check if: 1) All the R files has man file or an alias. 2) All aliases belongs to
functions. 3) If there are dublicated aliases.
For function "checkExamples": reads from the man directory all the Rd files, then read from each
file the examples and then run each of them. If you want to print the errors in any file then set
"print.errors=file_name" or in the standard error "print.errors=stderr()" and then you will see all the
errors for every file. For succeed run of your code you should first run "library(PACKAGE_NAME)".
The argument "print.names" it is very helpful because if any of you function crashes R during running you will never know which one was. So setting it "TRUE", it will print the name of each file
before runnign it’s example.It might crash, but you will know which file. Remember that there
always an error timeout so it might didn’t crash the current file but one from the previous.
For function checkTF: reads from the man directory all the Rd files, then read from each file the
examples and checks if any examples has the values "T" and "F" instead "TRUE" and "FALSE".
The "T","F" is wrong.
For function checkUsage: reads from the man directory all the Rd files and for each man check
if the usage section has the right signature for the functions from the R directory. This functions
has 2 limitations: 1) each function should be in one R file with name function_name.R and only
this function can be inside the file. 2) if you want multiple functions inside this file then the main
function should the first on top.
Value
For function "checkNamespace": a vector with the names of missing R files.
For function "checkAliases": a list with 3 fields.
Missing Man files
A vector with the names of the missing Rd files.
Missing R files
A vector with the names of the missing R files.
Duplicate alias
A vector with the names of the dublicate aliases.
For function "checkExamples": a list with 2 fields
Errors
A character vector with the names of the Rd files that produced an error.
Big Examples
A character vector with the names of the Rd files that has big examples per line.
For function "checkTF": a list with 2 fields
Check whether a square matrix is symmetric
TRUE
A character vector with the names of the Rd files that has "T".
FALSE
A character vector with the names of the Rd files that has "F".
23
For function "checkUsage": a list with 2 fields
missing functions
A character vector with the name of the file that is missing and the Rd file that
is found.
missmatch functions
A character vector with the name of the file that has missmatch function and the
Rd file that is found.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
read.directory, AddToNamespace, sourceR, sourceRd, read.examples
Examples
## Not run:
# for example:
# for example:
# for example:
# system.time(
# system.time(
# system.time(
# system.time(
# system.time(
path.namespace="C:\some_file\NAMESPACE"
path.rfolder="C:\some_file\R\"
path.man="C:\some_file\man\"
a<-checkNamespace(path.namespace,path.rfolder) )
b<-checkAliases(path.man,path.rfolder) )
b<-checkExamples(path.man) )
b<-checkExamples(path.man,2) )
b<-checkTF(path.man) )
## End(Not run)
Check whether a square matrix is symmetric
Check whether a square matrix is symmetric
Description
Check whether a square matrix is symmetric.
Usage
is.symmetric(x)
Arguments
x
A square matrix with data.
24
Cholesky decomposition of a square matrix
Details
Instead of going through the whole matrix, the function will stop if the first disagreement is met.
Value
A boolean value, TRUE of FALSE.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
cholesky, cora, cova
Examples
x <-matrix( rnorm( 100 * 400), ncol = 400 )
s1 <- cor(x)
is.symmetric(s1)
x <- x[1:100, ]
is.symmetric(x)
x<-s1<-NULL
Cholesky decomposition of a square matrix
Cholesky decomposition of a square matrix
Description
Cholesky decomposition of a square matrix.
Usage
cholesky(x,parallel = FALSE)
Arguments
x
A square positive definite matrix.
parallel
A boolean value for parallel version.
Details
The Cholesky decomposition of a square positive definite matrix is computed. The use of parallel
is suggested for matrices with dimensions of 1000 or more.
Circular or angular regression
25
Value
An upper triangular matrix.
Author(s)
Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
See Also
is.symmetric
Examples
x = matrix(rnorm(1000 * 50), ncol = 50)
s = cov(x)
system.time(a1 <- cholesky(s))
system.time(a2 <- chol(s))
all.equal(a1[upper.tri(a1)], a2[upper.tri(a2)])
x <- NULL
s <- NULL
a1 <- NULL
a2 <- NULL
Circular or angular regression
Circular or angular regression
Description
Regression with circular dependent variable and Euclidean or categorical independent variables.
Usage
spml.reg(y, x, tol = 1e-07, seb = FALSE)
Arguments
y
x
tol
seb
The dependent variable, it can be a numerical vector with data expressed in
radians or it can be a matrix with two columns, the cosinus and the sinus of
the circular data. The benefit of the matrix is that if the function is to be called
multiple times with the same response, there is no need to transform the vector
every time into a matrix.
The independent variable(s). Can be Euclidean or categorical (factor variables).
The tolerance value to terminatate the Newton-Raphson algorithm.
Do you want the standard error of the estimates to be returned? TRUE or
FALSE.
26
Circular or angular regression
Details
The Newton-Raphson algorithm is fitted in this regression as described in Presnell et al. (1998).
Value
A list including:
iters
The number of iterations required until convergence of the EM algorithm.
be
The regression coefficients.
seb
The standard errors of the coefficients.
loglik
The value of the maximised log-likelihood.
seb
The covariance matrix of the beta values.
Author(s)
Michail Tsagris and Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
References
Presnell Brett, Morrison Scott P. and Littell Ramon C. (1998). Projected multivariate linear models
for directional data. Journal of the American Statistical Association, 93(443): 1068-1077.
See Also
spml.mle, iag.mle, acg.mle
Examples
x <- rnorm(100)
z <- cbind(3 + 2 * x, 1 -3 * x)
y <- cbind( rnorm(100,z[ ,1], 1), rnorm(100, z[ ,2], 1) )
y <- y / sqrt( rowsums(y^2) )
a1 <- spml.reg(y, x)
y <- atan( y[, 2] / y[, 1] ) + pi * I(y[, 1] < 0)
a2 <- spml.reg(y, x)
Circular-linear correlation
Circular-linear correlation
Circular-linear correlation
Description
It calculates the squared correlation between a circular and one or more linear variables.
Usage
circlin.cor(theta, x)
Arguments
theta
x
A circular variable expressed in radians.
The linear variable or a matrix containing many linear variables.
Details
The squared correlation between a circular and one or more linear variables is calculated.
Value
A matrix with as many rows as linear variables including:
R-squared
p-value
The value of the squared correlation.
The p-value of the zero correlation hypothesis testing.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.
See Also
spml.reg
Examples
phi <- rvonmises(50, 2, 20, rads = TRUE)
x <- 2 * phi + rnorm(50)
y <- matrix(rnorm(50 * 5), ncol = 5)
circlin.cor(phi, x)
circlin.cor(phi, y)
y <- NULL
27
28
Column and row wise coefficients of variation
Column and row wise coefficients of variation
Column and row wise coefficients of variation
Description
Column and row wise coefficients of variation.
Usage
colcvs(x, ln = FALSE, unbiased = FALSE)
rowcvs(x, ln = FALSE, unbiased = FALSE)
Arguments
x
A numerical matrix with the data.
ln
If you have log-normally distributed data (or assume you do), then set this to
TRUE.
unbiased
A boolean variable indicating whether the unbiased for shpould be returned.
This is applicable in case of small samples.
Details
The colum-wise coefficients of variation are calculated.
Value
A vector with the coefficient of variation for each column or row.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
colsums, colVars
Examples
m <- rnorm(100, 10)
x <- matrix(rnorm(100 * 100, m, 1), ncol = 100)
a1 <- colcvs(x)
a2 <- colcvs(x[1:25, ], unbiased = TRUE)
a3 <- colcvs( exp(x), ln = TRUE)
x <- NULL
Column and row-wise Any/All
29
Column and row-wise Any/All
Column and row-wise Any
Description
Column and row-wise Any/All of a matrix.
Usage
colAny(x)
rowAny(x)
colAll(x, parallel = FALSE)
rowAll(x, parallel = FALSE)
Arguments
x
A logical matrix with the data.
parallel
Do you want the computations to take place in parallel? The default value is
FALSE.
Details
The functions is written in C++ in order to be as fast as possible.
Value
A vector where item "i" is true if found Any/All true in column/row "i". Otherwise false.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
med, colMedians, colMeans (buit-in R function)
Examples
x <- matrix(as.logical(rbinom(100*100,1,0.5)),100,100)
system.time( a<-colAny(x) )
system.time( b<-apply(x,2,any) )
all.equal(a,b)
system.time( a<-rowAny(x) )
system.time( b<-apply(x,1,any) )
all.equal(a,b)
30
Column and row-wise means of a matrix
system.time( a<-colAll(x) )
system.time( b<-apply(x,2,all) )
all.equal(a,b)
a<-b<-x<-NULL
Column and row-wise means of a matrix
Column and row-wise means of a matrix
Description
Column and row-wise means of a matrix.
Usage
colmeans(x, parallel = FALSE)
rowmeans(x)
colhameans(x, parallel = FALSE)
rowhameans(x)
Arguments
x
A numerical matrix with data.
parallel
Do you want to do it in parallel in C++? TRUE or FALSE.
Value
A vector with the column or row arithmetic or harmonic means.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colsums, rowsums, colMins, colMedians, colMads
Examples
x <- matrix(rpois(100 * 100, 10),ncol = 100)
x1 <- colmeans(x)
x2 <- colMeans(x)
all.equal(x1,x2)
x1 <- rowmeans(x)
x2 <- rowMeans(x)
Column and row-wise medians
all.equal(x1,x2)
system.time( colhameans(x) )
system.time( rowhameans(x) )
x<-x1<-x2<-NULL
Column and row-wise medians
Column and row-wise medians
Description
Column and row-wise medians of a matrix.
Usage
colMedians(x,na.rm = FALSE, parallel = FALSE)
rowMedians(x, parallel = FALSE)
Arguments
x
A matrix with the data.
parallel
Do you want to do it in parallel in C++? TRUE or FALSE.
na.rm
TRUE or FAlSE for remove NAs if exists.
Details
The functions is written in C++ in order to be as fast as possible.
Value
A vector with the column medians.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
med, colVars, colMeans (buit-in R function)
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
a <- apply(x, 2, median)
b1 <- colMedians(x)
all.equal(as.vector(a), b1)
x<-a<-b1<-NULL
31
32
Column and row-wise nth smallest value of a matrix/vector
Column and row-wise nth smallest value of a matrix/vector
Column and row-wise nth smallest value of a matrix/vector
Description
Column and row-wise nth smallest value of a matrix/vector.
Usage
colnth(x,elems, parallel = FALSE)
rownth(x,elems, parallel = FALSE)
nth(x, k,descending = FALSE,index.return = FALSE,na.rm = FALSE)
Arguments
x
A matrix with the data.
elems
An integer vector with the kth smallest number to be returned for each column/row.
k
The kth smallest/biggest number to be returned.
descending
A boolean value (TRUE/FALSE) for descending order (biggest number). By
default is ascending (smallest number).
index.return
Return the index of the kth smallest/biggest number.
parallel
Do you want to do it in parallel in C++? TRUE or FALSE only for col-row wise.
na.rm
TRUE or FAlSE for remove NAs if exists. Only for function "nth".
Details
The functions is written in C++ in order to be as fast as possible.
Value
For "colnth" , "rownth": A vector with the column/row nth
For "nth": The nth value.
Author(s)
Manos Papadakis <papadakm95@gmail.com>
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
med, colMedians, colMeans (buit-in R function)
Column and row-wise Order - Sort Indices
33
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
elems <- sample(1:100,100,TRUE)
system.time( colnth(x,elems) )
system.time( rownth(x,elems) )
x <- rnorm(1000)
nth(x, 500)
sort(x)[500]
x<-elems<-NULL
Column and row-wise Order - Sort Indices
Column and row-wise Order - Sort Indices
Description
Column and row-wise Order - Sort Indices.
Usage
colOrder(x,stable=FALSE,descending=FALSE, parallel = FALSE)
rowOrder(x,stable=FALSE,descending=FALSE, parallel = FALSE)
Order(x,stable=FALSE,descending=FALSE,partial = NULL)
Arguments
x
A matrix with numbers or a numeric/character vector.
stable
A boolean value for using a stable sorting algorithm.
descending
A boolean value (TRUE/FALSE) for sorting the vector in descending order. By
default sorts the vector in ascending.
parallel
A boolean value for parallel version.
partial
A boolean value for partial sorting.
Details
The function applies "order" in a column or row-wise fashion or Order a vector. If you want the
same results as R’s, then set "stable=TRUE" because "stable=FALSE" uses a sorting algorithm that
it is not stable like R’s sort. But it is faster to use the default. This verion is faster for large data,
more than 300.
Value
For "colOrder" and "rowOrder" a matrix with integer numbers. The result is the same as apply(x,
2, order) or apply(x, 1, order).
For "Order" sort the vector and returns the indices of each element that it has before the sorting.
The result is the same as order(x) but for the same exactly results set argument "stable" to "TRUE".
34
Column and row-wise products
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colsums, coldiffs, colMedians, colprods
Examples
x <- matrix( runif(10 * 10), ncol = 10 )
colOrder(x)
apply(x, 2, order)
rowOrder(x)
t(apply(x, 1, order))
y <- rnorm(100)
b <- Order(y)
a <- order(y)
all.equal(a,b) ## false because it is not stable
b <- Order(y,stable=TRUE)
all.equal(a,b) ## true because it is stable
x<-y<-b<-a<-NULL
Column and row-wise products
Column and row-wise products
Description
Column and row-wise products.
Usage
colprods(x)
rowprods(x)
Arguments
x
A matrix with numbers.
Details
The product of the numbers in a matrix is returned either column-wise or row-wise.
Value
A vector with the column or the row products.
Column and row-wise range of values of a matrix
35
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colsums, coldiffs, colMedians
Examples
x <- matrix( runif(100 * 10), ncol = 10 )
colprods(x)
rowprods(x)
x<-NULL
Column and row-wise range of values of a matrix
Column and row-wise range of values of a matrix.
Description
Column and row-wise range of values of a matrix.
Usage
colrange(x, cont = TRUE)
rowrange(x, cont = TRUE)
Arguments
x
A numerical matrix with data.
cont
If the data are continuous, leave this TRUE and it will return the range of values
for each variable (column). If the data are integers, categorical, or if you want
to find out the number of unique numbers in each column set this to FALSE.
Value
A vector with the relevant values.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colMins, colMaxs, rowMins, rowMaxs, nth, colMedians, colVars, sort_mat
36
Column and row-wise ranks
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
a1 <- colrange(x)
a2 <- apply(x, 2, function(x) diff( range(x)) )
all.equal(a1, a2)
a1 <- rowrange(x)
a2 <- apply(x, 1, function(x) diff( range(x)) )
all.equal(a1, a2)
x<-a1<-a2<-NULL
Column and row-wise ranks
Column and row-wise ranks
Description
Column and row-wise ranks.
Usage
colRanks(x,method = "average",descending = FALSE,stable = FALSE, parallel = FALSE)
rowRanks(x,method = "average",descending = FALSE,stable = FALSE, parallel = FALSE)
Arguments
x
A mumerical matrix with the data.
parallel
A boolean value for parallel version.
method
a character string for choosing method. Must be one of "average", "min", "max",
"first".
descending
A boolean value (TRUE/FALSE) for sorting the vector in descending order. By
default sorts the vector in ascending.
stable
A boolean value (TRUE/FALSE) for choosing a stable sort algorithm. Stable
means that discriminates on the same elements. Only for the method "first".
Details
For each column or row of a matrix the ranks are calculated and they are returned. The initial matrix
is gone.
Value
A matrix with the column or row-wise ranks.
Column and row-wise Shuffle
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
Rank, correls
Examples
x <- matrnorm(100, 10)
a1 <- colRanks(x)
a2 <- apply(x, 2, rank)
b1 <- rowRanks(x)
b2 <- apply(x, 1, rank)
x<-a1<-a2<-b1<-b2<-NULL
Column and row-wise Shuffle
Column and row-wise Shuffle
Description
Column and row-wise shuffle of a matrix.
Usage
colShuffle(x)
rowShuffle(x)
Arguments
x
A matrix with the data.
Details
The functions is written in C++ in order to be as fast as possible.
Value
A vector with the column/row Shuffle.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
37
38
Column and row-wise sums of a matrix
See Also
med, colVars, colMeans (buit-in R function)
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
system.time( colShuffle(x) )
system.time( rowShuffle(x) )
x<-NULL
Column and row-wise sums of a matrix
Column and row-wise sums of a matrix
Description
Column and row-wise sums of a matrix.
Usage
colsums(x,indices = NULL, parallel = FALSE)
rowsums(x,indices = NULL, parallel = FALSE)
Arguments
x
A numerical matrix with data.
indices
An integer vector with the indices to sum the columns/rows.
parallel
Do you want to do it in parallel in C++? TRUE or FALSE. Doens’t work with
argument "indices".
Value
A vector with sums.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colMedians, colmeans, colVars
Column and row-wise tabulate
39
Examples
x <- matrix(rpois(500 * 100, 10),ncol = 100)
x1 <- colsums(x)
x2 <- colSums(x)
all.equal(x1,x2)
x1 <- rowsums(x)
x2 <- rowSums(x)
all.equal(x1,x2)
x<-x1<-x2<-NULL
Column and row-wise tabulate
Column and row-wise tabulate
Description
Column and row-wise tabulate of a matrix.
Usage
colTabulate(x, max_number = max(x))
rowTabulate(x, max_number = max(x))
Arguments
x
An integer matrix with the data. The numbers must start from 1, i.e. 1, 2, 3, 4,...
No zeros are allowed. Anything else may cause a crash.
max_number
The maximum value of vector x. If you know which is the max number use this
argument for faster results or by default max(x).
Details
The functions is written in C++ in order to be as fast as possible.
Value
A matrix where in each column the command "tabulate" has been performed. The number of rows
of the returned matrix will be equal to the max_number if given. Otherwise, the functions will find
this number.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colShuffle, colVars, colmeans
40
Column and row-wise variances and standard deviations
Examples
x <- matrix( rbinom(100 * 100, 4, 0.5), ncol = 100 )
system.time( colTabulate(x) )
x <- t(x)
system.time( rowTabulate(x) )
x<-NULL
Column and row-wise variances and standard deviations
Column and row-wise variances and standard deviations of a matrix
Description
Column and row-wise variances and standard deviations of a matrix
Usage
colVars(x, suma = NULL, std = FALSE, parallel = FALSE)
rowVars(x, suma = NULL, std = FALSE)
groupcolVars(x, ina, std = FALSE)
Arguments
x
A matrix with the data.
suma
If you already have the column sums vector supply it, otherwise leave it NULL.
ina
A numerical vector specifying the groups. If you have numerical values, do not
put zeros, but 1, 2, 3 and so on.
std
A boolean variable specyfying whether you want the variances (FALSE) or the
standard deviations (TRUE) of each column.
parallel
Should parallel implentations take place in C++? The default value is FALSE.
Details
We found this in stackoverflow and was created by David Arenburg. We then modified the function
to match the sums type formula of the variance, which is faster.
Value
A vector with the column variances or standard deviations.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Column and rows-wise mean absolute deviations
41
See Also
colmeans, colMedians, colrange
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
a2 <- colVars(x)
groupcolVars( as.matrix(iris[, 1:4]), as.numeric(iris[, 5]) )
x<-a2<-NULL
Column and rows-wise mean absolute deviations
Column and row-wise mean absolute deviations
Description
Column and row-wise mean absolute deviations.
Usage
colMads(x,parallel = FALSE)
rowMads(x,parallel = FALSE)
Arguments
x
A matrix with the data.
parallel
A boolean value for parallel version.
Details
The functions is written in C++ in order to be as fast as possible.
Value
A vector with the column-wise mean absolute deviations.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
colMedians, rowMedians, colVars, colmeans, colMeans (buit-in R function)
42
Column-row wise minima and maxima of two matrices
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
system.time( a <- colMads(x) )
x<-NULL
Column-row wise minima and maxima of two matrices
Column-row wise minima and maxima of two matrices
Description
Column-row wise minima and maxima of two matrices.
Usage
colPmax(x, y)
colPmin(x, y)
Arguments
x
A numerical vector with numbers.
y
A numerical vector with numbers.
Details
The parallel minima or maxima are returned. This are the same as the base functions pmax and
pmin.
Value
A numerical vector/matrix with numbers, whose length is equal to the length of the initital matrices
containing the maximum or minimum between each pair.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
sort_mat, Sort, colMins, colMaxs, colMedians
Column-wise differences
43
Examples
x <- matrix(rnorm(100),10,10)
y <- matrix(rnorm(100),10,10)
colPmax(x, y)
colPmin(x, y)
x<-y<-NULL
Column-wise differences
Column-wise differences
Description
Column-wise differences.
Usage
coldiffs(x)
Arguments
A matrix with numbers.
x
Details
This function simply does this function x[, -1] - x[, -k], where k is the last column of the matrix x.
But it does it a lot faster. That is, 2nd column - 1st column, 3rd column - 2nd column, and so on.
Value
A matrix with one column less containing the differences between the successive columns.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
Dist, dista, colmeans
Examples
x <- matrix( rnorm(50 * 10), ncol = 10 )
coldiffs(x)
x<-NULL
44
Column-wise kurtosis and skewness coefficients
Column-wise kurtosis and skewness coefficients
Column-wise kurtosis and skewness coefficients
Description
Column-wise kurtosis and skewness coefficients.
Usage
colkurtosis(x, pvalue = FALSE)
colskewness(x, pvalue = FALSE)
Arguments
x
A matrix with the data, where the rows denote the samples and the columns are
the variables.
pvalue
If you want a hypothesis test that the skewness or kurtosis are significant set this
to TRUE. This checks whether the skewness is significantly different from 0 and
whether the kurtosis is significantly different from 3.
Details
The skewness and kurtosis coefficients are calculated. For the skewness coefficient we use the
sample unbiased version of the standard deviation. For the kurtosis, we do not subtract 3.
Value
If "pvalue" is FALSE, a vector with the relevant coefficient. Otherwise a matrix with two columns.
The kurtosis or skewness coefficient and the p-value from the hypothesis test that they are significantly different from 3 or 0 respectively.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
skew, skew.test2, colMedians, colmeans, colVars, sftests
Column-wise matching coefficients
45
Examples
## 200 variables, hence 200 F-tests will be performed
x = matrix( rnorm(200 * 50), ncol = 50 )
## 200 observations in total
system.time( colkurtosis(x) )
system.time( colskewness(x) )
x <- NULL
Column-wise matching coefficients
Column-wise matching coefficients
Description
Column-wise matching coefficients.
Usage
match.coefs(x, y = NULL, ina, type = "jacc")
Arguments
x
A matrix with the data, where the rows denote the samples and the columns are
the variables.
y
A second matrix with the data of the second group. If this is NULL (default
value) then the argument ina must be supplied. Notice that when you supply the
two matrices the procedure is two times faster.
ina
A numerical vector with 1s and 2s indicating the two groups. Be careful, the
function is designed to accept only these two numbers. In addition, if your "y"
is NULL, you must specify "ina".
type
This denotes the type of matching coefficient to calculate. For the Jaccard index
put "jacc". For the simple matching coefficient put "smc" or else both of them
will be calculated.
Details
Two matrices are given as imput and for each column matching coefficients are calculated, either
the Jaccard or the simple matching coefficient or both.
Value
A matrix with one or two columns, depending on the type you have specified. If you specify "both",
there will be two columns, if you specify "jacc" or "smc" then just one column.
46
Column-wise minimum and maximum
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
odds, colTabulate
Examples
x
y
a
x
y
<<<<<-
matrix(rbinom(400 * 10, 1, 0.5), ncol = 10)
matrix(rbinom(400 * 10, 1, 0.5), ncol = 10)
match.coefs(x, y, type = "both")
NULL
NULL
Column-wise minimum and maximum
Column-wise minimum and maximum of a matrix
Description
Column-wise minimum and maximum of a matrix.
Usage
colMins(x, value = FALSE, parallel = FALSE)
colMaxs(x, value = FALSE, parallel = FALSE)
colMinsMaxs(x)
Arguments
x
A numerical matrix with data.
value
If the value is FALSE it returns the indices of the minimum/maximum, otherwise
it returns the minimum and maximum values.
parallel
Do you want to do it in parallel in C++? TRUE or FALSE. The parallel will
return the minimum/maximum value only. It will never return the indices.
Value
A vector with the relevant values.
Column-wise MLE of some univariate distributions
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, rowMaxs, nth, colrange, colMedians, colVars, sort_mat
Examples
x <- matrix( rnorm(100 * 200), ncol = 200 )
s1 <- colMins(x)
s2 <- apply(x, 2, min)
s1 <- colMaxs(x)
s2 <- apply(x, 2, max)
s1 <- colMinsMaxs(x)
s2 <- c(apply(x, 2, min), apply(x, 2, max))
x<-s1<-s2<-NULL
Column-wise MLE of some univariate distributions
Column-wise MLE of some univariate distributions
Description
Column-wise MLE of some univariate distributions.
Usage
colexpmle(x)
colexp2.mle(x)
colgammamle(x, tol = 1e-07)
colinvgauss.mle(x)
collaplace.mle(x)
collindley.mle(x)
colmaxboltz.mle(x)
colnormal.mle(x)
colpareto.mle(x)
colpois.mle(x)
colrayleigh.mle(x)
colvm.mle(x, tol = 1e-07)
colweibull.mle(x, tol = 1e-09, maxiters = 100, parallel = FALSE)
colnormlog.mle(x)
47
48
Column-wise MLE of some univariate distributions
Arguments
x
A numerical matrix with data. Each column refers to a different vector of observations of the same distribution. For exponential, 2 parameter exponential,
Weibull, gamma, inverse Gaussian, Maxwell-Boltzman, Lindley, Rayleigh and
Pareto distributions, the numbers must be greater than zero. For the Poisson and
geometric distributions, the numbers must be integers, 0, 1, 2,... For the Normal and Laplace distribution the numbers can take any value. The von Mises
distribution takes values beween 0 and 2 * pi (radians).
tol
The tolerance value to terminate the Newton-Fisher algorithm.
maxiters
The maximum number of iterations to implement.
parallel
Do you want to calculations to take place in parallel? The default value is
FALSE
Details
For each column, the same distribution is fitted and its parameter and log-likelihood are computed.
Value
A matrix with two, three or five (for the colnormlog.mle) columns. The first one or the first two contain the parameter(s) of the distribution and the second or third column the relvant log-likelihood.
Author(s)
Michail Tsagris and Stefanos Fafalios
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Stefanos Fafalios
<stefanosfafalios@gmail.com>
References
Kalimuthu Krishnamoorthy, Meesook Lee and Wang Xiao (2015). Likelihood ratio tests for comparing several gamma distributions. Environmetrics, 26(8):571-583.
N.L. Johnson, S. Kotz \& N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1
(2nd Edition).
N.L. Johnson, S. Kotz \& N. Balakrishnan (1970). Distributions in statistics: continuous univariate
distributions, Volume 2
Sharma V. K., Singh S. K., Singh U. \& Agiwal V. (2015). The inverse Lindley distribution: a
stress-strength reliability model with application to head and neck cancer data. Journal of Industrial
and Production Engineering, 32(3): 162-173.
See Also
vm.mle, poisson.mle, normal.mle, gammamle
Column-wise true/false value
Examples
x
a
b
x
<<<<-
matrix(rnorm(1000 * 50), ncol = 50)
colnormal.mle(x)
collaplace.mle(x)
NULL
Column-wise true/false value
Column-wise true/false value of a matrix
Description
Column-wise true/false value of a matrix.
Usage
colTrue(x)
colFalse(x)
colTrueFalse(x)
Arguments
x
A logical matrix with data.
Value
An integer vector where item "i" is the number of the true/false values of "i" column.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, rowFalse, nth, colrange, colMedians, colVars, sort_mat, rowTrue
Examples
x <- matrix(as.logical(rbinom(100*100,1,0.5)),100,100)
s1 <- colTrue(x)
s1 <- colFalse(x)
s1 <- colTrueFalse(x)
x<-s1<-NULL
49
50
Column-wise uniformity Watson test for circular data
Column-wise uniformity Watson test for circular data
Column-wise uniformity tests for circular data
Description
Column-wise uniformity tests for circular data.
Usage
colwatsons(u)
Arguments
u
A numeric matrix containing the circular data which are expressed in radians.
Each column is a different sample.
Details
These tests are used to test the hypothesis that the data come from a circular uniform distribution.
The Kuiper test is much more time consuming and this is why it not implemented yet. Once we
figure out a way to make it fast, we will incldue it.
Value
A matrix with two columns, the value of the test statistic and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, pg. 153-55
(Kuiper’s test) & 156-157 (Watson’s test).
See Also
watson, vmf.mle, rvonmises
Examples
x <- matrix( rvonmises(n = 50 * 10, m = 2, k = 0), ncol = 10 )
colwatsons(x)
x <- NULL
Column-wise Yule’s Y (coefficient of colligation)
51
Column-wise Yule’s Y (coefficient of colligation)
Column-wise Yule’s Y (coefficient of colligation)
Description
Column-wise Yule’s Y (coefficient of colligation).
Usage
col.yule(x, y = NULL, ina)
Arguments
x
A matrix with 0 and 1. Every column refers to a different sample or variable.
y
A second matrix, of the same dimensions as x, with 0 and 1. Every column
refers to a different sample or variable.
ina
If y is NULL, ina must be specified. This is a numeric vector with 1s and 2s,
indicating the group of each row.
Details
Yule’s coefficient of colligation is calculated for every column.
Value
A vector with Yule’s Y, one for every column of x is returned.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Yule G. Udny (1912). On the Methods of Measuring Association Between Two Attributes. Journal
of the Royal Statistical Society, 75(6):579-652.
See Also
yule, odds
Examples
x <- matrix(rbinom(300 * 10, 1, 0.5), ncol = 10)
ina <- rep(1:2, each = 150)
col.yule( x, ina = ina )
52
Correlation based forward regression
Correlation based forward regression
Correlation based forward regression.
Description
Correlation based forward regression.
Usage
cor.fsreg(y, x, threshold = 0.05, tolb = 2, tolr = 0.02, stopping = "BIC")
Arguments
y
A numerical vector.
x
A matrix with data, the predictor variables.
threshold
The significance level, set to 0.05 by default. Bear in mind that the logarithm of
it is used, as the logarithm of the p-values is calculated at every point. This will
avoid numerical overflows and small p-values, less than the machine epsilon,
being returned as zero.
tolb
If we see only the significane of the variables, many may enter the linear regression model. For this reason, we also use the BIC as a way to validate the
inclusion of a candidate variable. If the BIC difference between two successive
models is less than the tolerance value, the variable will not enter the model,
even if it statistically significant. Set it to 0 if you do not want this extra check.
tolr
This is an alternative to the BIC change and it uses the adjusted coefficient of
determination. If the increase in the adjusted R2 is more than the tolr continue.
stopping
This refers to the type of extra checking to do. If you want the BIC check, set
it to "BIC". If you want the adjusted R2 check set this to "ar2". Or, if you
want both of them to take place, both of these criteria to be satisfied make this
"BICR2".
Details
The forward regression tries one by one the variables using the F-test, basically partial F-test every
time for the latest variable. This is the same as testing the significance of the coefficient of this latest
enetered variable. Alternatively the correlation can be used and this case the partial correlation
coefficient. There is a direct relationship between the t-test statistic and the partial correlation
coefficient. Now, instead of having to calculate the test statistic, we calculate the partial correlation
coefficient. Using Fisher’s z-transform we get the variance imediately. The partial correlation
coefficient, using Fisher’s z-transform, and the partial F-test (or the coefficient’s t-test statistic) are
not identical. They will be identical for large sample sizes though.
53
Correlation between pairs of variables
Value
A matrix with three columns, the index of the selected variables, the logged p-value and the the test
statistic value and the BIC or adjusted R2 of each model. In the case of stopping="BICR2" both of
these criteria will be returned.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
See Also
score.glms, univglms, logistic_only,
poisson_only, regression
Examples
## 200 variables, hence 200 univariate regressions are to be fitted
x <- matrnorm(200, 100)
y <- rnorm(200)
system.time( cor.fsreg(y, x) )
x <- NULL
Correlation between pairs of variables
Correlation between pairs of variables
Description
Correlations between pairs of variables.
Usage
corpairs(x, y, rho = NULL, logged = FALSE, parallel = FALSE)
Arguments
x
A matrix with real valued data.
y
A matrix with real valued data whose dimensions match those of x.
rho
This can be a vector of assumed correlations (equal to the number of variables
or the columns of x or y) to be tested. If this is not the case, leave it NULL and
only the correlations will be returned.
54
Correlation between pairs of variables
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)? This is
taken into account only if "rho" is a vector.
parallel
Should parallel implentations take place in C++? The default value is FALSE.
Details
The paired correlations are calculated. For each column of the matrices x and y the correlation
between them is calculated.
Value
A vector of correlations in the case of "rho" being NULL, or a matrix with two extra columns, the
test statistic and the (logged) p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Lambert Diane (1992). Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 34(1):1-14.
Johnson Norman L., Kotz Samuel and Kemp Adrienne W. (1992). Univariate Discrete Distributions
(2nd ed.). Wiley
Cohen, A. Clifford (1960). Estimating parameters in a conditional Poisson distribution. Biometrics.
16:203-211.
Johnson, Norman L. Kemp, Adrianne W. Kotz, Samuel (2005). Univariate Discrete Distributions
(third edition). Hoboken, NJ: Wiley-Interscience.
See Also
correls, allbetas, mvbetas
Examples
x <- matrnorm(100, 100)
y <- matrnorm(100, 100)
system.time( corpairs(x, y) )
a <- corpairs(x, y)
x <- NULL
y <- NULL
55
Correlations
Correlation between a vector and a set of variables
Correlations
Description
Correlation between a vector and a set of variables.
Usage
correls(y, x, type = "pearson", a = 0.05, rho = 0)
groupcorrels(y, x, type = "pearson", ina)
Arguments
y
A numerical vector.
x
A matrix with the data.
type
The type of correlation you want. "pearson" and "spearman" are the two supported types for the "correls" because their standard error is easily calculated.
For the "groupcorrels" you can also put "kendall" because no hypothesis test is
performed in that function.
a
The significance level used for the confidence intervals.
rho
The value of the hypothesised correlation to be used in the hypothesis testing.
ina
A factor variable or a numeric variable idicating the group of each observation.
Details
The functions uses the built-in function "cor" which is very fast and then includes confidence intervals and produces a p-value for the hypothesis test.
Value
For the "correls" a matrix with 5 column; the correlation, the p-value for the hypothesis test that
each of them is eaqual to "rho", the test statistic and the $a/2%$ lower and upper confidence limits.
For the "groupcorrels" a matrix with rows equal to the number of groups and columns equal to the
number of columns of x. The matrix contains the correlations only, no statistical hypothesis test is
performed.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
allbetas, univglms
56
Covariance and correlation matrix
Examples
x <- matrnorm(60, 100 )
y <- rnorm(60)
r <- cor(y, x) ## correlation of y with each of the xs
a <- allbetas(y, x) ## the coefficients of each simple linear regression of y with x
b <- correls(y, x)
ina <- rep(1:2, each = 30)
b2 <- groupcorrels(y, x, ina = ina)
x <- NULL
Covariance and correlation matrix
Fast covariance and correlation matrix calculation
Description
Fast covariance and correlation matrix calculation.
Usage
cova(x)
cora(x)
Arguments
x
A matrix with data. It has to be matrix, if it is data.frame for example the
function does not turn it into a matrix.
Details
The calculations take place faster than the built-in functions cor as the number of variables increases. For a few tens of variables. This is true if the number of variables is high, say from 500
and above. The "cova" on the other hand is always faster.
For the correlation matrix we took the code from here
https://stackoverflow.com/questions/18964837/fast-correlation-in-r-using-c-and-parallelization/18965892#18965892
Value
The covariance or correlation matrix.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Cox confidence interval for the ratio of two Poisson variables
57
See Also
colVars, cor, cov
Examples
x <- matrnorm( 100, 100 )
s1 <- cov(x)
s2 <- cova(x)
all.equal(s1, s2)
x <- NULL
Cox confidence interval for the ratio of two Poisson variables
Cox confidence interval for the ratio of two Poisson variables
Description
Cox confidence interval for the ratio of two Poisson variables.
Usage
cox.poisrat(x, y, alpha = 0.05)
col.coxpoisrat(x, y, alpha = 0.05)
Arguments
x
A numeric vector or a matrix with count data.
y
A numeric vector or a matrix with count data.
alpha
The 1 - confidence level. The default value is 0.05.
Details
Cox confidence interval for the ratio of two Poisson means is calculated.
Value
For the cox.poisrat a vector with three elements, the ratio and the lower and upper confidence
interval limits. For the col.coxpoisrat a matrix with three columns, the ratio and the lower and
upper confidence interval limits.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
58
Cross-Validation for the k-NN algorithm
References
Krishnamoorthy K., Peng J. and Zhang D. (2016). Modified large sample confidence intervals
for Poisson distributions: Ratio, weighted average, and product of means. Communications in
Statistics-Theory and Methods, 45(1): 83-97.
See Also
correls, Table
Examples
x <- rpois(100, 10)
y <- rpois(100, 10)
cox.poisrat(x, y)
Cross-Validation for the k-NN algorithm
Cross-Validation for the k-NN algorithm
Description
Cross-Validation for the k-NN algorithm.
Usage
knn.cv(folds = NULL, nfolds = 10, stratified = FALSE, seed = FALSE, y, x, k,
dist.type = "euclidean", type = "C", method = "average", freq.option = 0,
pred.ret = FALSE, mem.eff = FALSE)
Arguments
folds
A list with the indices of the folds.
nfolds
The number of folds to be used. This is taken into consideration only if "folds"
is NULL.
stratified
Do you want the folds to be selected using stratified random sampling? This
preserves the analogy of the samples of each group. Make this TRUE if you
wish, but only for the classification. If you have regression (type = "R"), do not
put this to TRUE as it will cause problems or return wrong results.
seed
If you set this to TRUE, the same folds will be created every time.
y
A vector of data. The response variable, which can be either continuous or
categorical (factor is acceptable).
x
A matrix with the available data, the predictor variables.
k
A vector with the possible numbers of nearest neighbours to be considered.
dist.type
The type of distance to be used, "euclidean" or "manhattan".
type
Do you want to do classification ("C") or regression ("R")?
Cross-Validation for the k-NN algorithm
59
method
If you do regression (type = "R"), then how should the predicted values be calculated? Choose among the average ("average"), median ("median") or the harmonic mean ("harmonic") of the closest neighbours.
freq.option
If classification (type = "C") and ties occur in the prediction, more than one class
have the same number of k nearest neighbours, there are three strategies available. Option 0 selects the first most frequent encountered. Option 1 randomly
selects the most frequent value, in the case that there are duplicates.
pred.ret
If you want the predicted values returned set this to TRUE.
mem.eff
Boolean value indicating a conservative or not use of memory. Lower usage of
memory/Having this option on will lead to a slight decrease in execution speed
and should ideally be on when the amount of memory in demand might be a
concern.
Details
The concept behind k-NN is simple. Suppose we have a matrix with predictor variables and a
vector with the response variable (numerical or categorical). When a new vector with observations
(predictor variables) is available, its corresponding response value, numerical or categorical, is to
be predicted. Instead of using a model, parametric or not, one can use this ad hoc algorithm.
The k smallest distances between the new predictor variables and the existing ones are calculated.
In the case of regression, the average, median, or harmonic mean of the corresponding response
values of these closest predictor values are calculated. In the case of classification, i.e. categorical
response value, a voting rule is applied. The most frequent group (response value) is where the new
observation is to be allocated.
This function does the cross-validation procedure to select the optimal k, the optimal number of
nearest neighbours. The optimal in terms of some accuracy metric. For the classification it is the
percentage of correct classification and for the regression the mean squared error.
Value
A list including:
preds
If pred.ret is TRUE the predicted values for each fold are returned as elements
in a list.
crit
A vector whose length is equal to the number of k and is the accuracy metric for
each k.
Author(s)
Marios Dimitriadis
R implementation and documentation: Marios Dimitriadis <kmdimitriadis@gmail.com>
References
Friedman J., Hastie T. and Tibshirani R. (2017). The elements of statistical learning. New York:
Springer.
Cover TM and Hart PE (1967). Nearest neighbor pattern classification. IEEE Transactions on
Information Theory. 13(1):21-27.
60
data.frame.to_matrix
Tsagris Michail, Simon Preston and Andrew T.A. Wood (2016). Improved classification for compositional data using the α-transformation. Journal of classification 33(2): 243-261.
See Also
knn, Dist, dista
Examples
x <- as.matrix(iris[, 1:4])
y <- iris[, 5]
mod <- knn.cv(folds = NULL, nfolds = 10, stratified = TRUE, seed = FALSE, y = y, x = x,
k = c(3, 4), dist.type = "euclidean", type = "C", method = "average",
freq.option = 0, pred.ret = FALSE, mem.eff = FALSE)
data.frame.to_matrix
Convert a dataframe to matrix
Description
Convert a dataframe to matrix.
Usage
data.frame.to_matrix(x,col.names = NULL,row.names = NULL)
Arguments
x
A Numeric matrix with data and NAs.
col.names
A boolean value for keeping the colnames for argument x or a character vector
for the new colnames.
row.names
A boolean value for keeping the rownames for argument x or a character vector
for the new rownames.
Details
This functions converts a dataframe to matrix. Even if there are factors, the function converts them
into numerical values. Attributes are not allowed for now.
Value
A matrix wich has the numrical values from the dataframe.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
Density of the multivariate normal and t distributions
61
See Also
Match, is.symmetric, permutation
Examples
data.frame.to_matrix(iris)
Density of the multivariate normal and t distributions
Density of the multivariate normal and t distributions
Description
Density of the multivariate normal and t distributions.
Usage
dmvnorm(x, mu, sigma, logged = FALSE)
dmvt(x, mu, sigma, nu, logged = FALSE)
Arguments
x
A numerical matrix with the data. The rows correspond to observations and the
columns to variables.
mu
The mean vector.
sigma
The covariance matrix.
nu
The degrees of freedom for the multivariate t distribution.
logged
Should the logarithm of the density be returned (TRUE) or not (FALSE)?
Details
The (log) density of the multivariate normal distribution is calculated for given mean vector and
covariance matrix.
Value
A numerical vector with the density values calculated at each vector (row of the matrix x).
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
rmvnorm, rmvt, mvnorm.mle, iag.mle
62
Design Matrix
Examples
x <- matrnorm(100, 20)
mu <- colmeans(x)
s <- cova(x)
a1 <- dmvnorm(x, mu, s)
a2 <- dmvt(x, mu, s, 1)
x <- NULL
Design Matrix
Design Matrix
Description
Design Matrix.
Usage
design_matrix(x, ones = TRUE)
Arguments
x
A character vector or a factor type vector or a dataframe. Do not supply a numerical vector.
ones
A boolean variable specifying whether to include the ones in the design matrix
or not. The default value is TRUE.
Details
This function implements the R’s "model.matrix" function and is used only when the x is a factor/charactervector or Dataframe.
Value
Returns the same matrix with model.matrix.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
See Also
model.matrix
63
Diagonal Matrix
Examples
a <- design_matrix( iris[, 5] )
b <- model.matrix( ~ iris[,5] ) ## R's built-in function
all.equal(as.vector(a),as.vector(b)) ## true
a<-b<-NULL
Diagonal Matrix
Diagonal Matrix
Description
Fill the diagonal of a matrix or create a diagonal and initialize it with a specific value.
Usage
Diag.fill(x,v=0)
Diag.matrix(len,v=0)
Arguments
x
A matrix with data.
len
Number of columns or rows.
v
Value or vector to initialize the diagonal of a matrix.By default "v=0".
Value
Diag.fill returns a diagonal matrix where all the elements in the diagonal are equal to "v".
Diag.matrix returns a diagonal matrix where has dimension "len,len" and all the elements in the diagonal are equal to "v". It is fast for huge matrices with dimensions more than [row,col] = [500,500]
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, colFalse, nth, rowrange, rowMedians, rowVars, sort_mat, colTrue
64
Distance between vectors and a matrix
Examples
x <- matrix(rbinom(100*100,1,0.5),100,100)
f
f
f
f
<<<<-
Diag.fill(x,1)
Diag.fill(x,1:100) ##equals to diag(x)<-1:100
Diag.matrix(100,1) ##equals to diag(1,100,100)
Diag.matrix(100,1:100) ##equals to diag(1:100,100,100)
f<-x<-NULL
Distance between vectors and a matrix
Distance between vectors and a matrix
Description
Distance between vectors and a matrix.
Usage
dista(xnew,x,type = "euclidean",k=0,index=FALSE,trans = TRUE,square = FALSE)
Arguments
xnew
A matrix with some data or a vector.
x
A matrix with the data, where rows denotes observations (vectors) and the columns
contain the variables.
type
This can be either "euclidean" or "manhattan".
k
Should the k smaller distances or their indices be returned? If k > 0 this will
happen.
index
In case k is greater than 0, you have the option to get the indices of the k smallest
distances.
trans
Do you want the returned matrix to be transposed? TRUE or FALSE.
square
If you choose "euclidean" as the method, then you can have the optino to return
the squared Euclidean distances by setting this argument to TRUE.
Details
The target of this function is to calculate the distances between xnew and x without having to
calculate the whole distance matrix of xnew and x. The latter does extra calculaitons, which can be
avoided.
Value
A matrix with the distances of each xnew from each vector of x. The number of rows of the xnew
and and the number of columns of xnew are the dimensions of this matrix.
65
Distance correlation
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
mahala, Dist, total.dist, total.dista
Examples
xnew
x <a <b <b <sum(
<- as.matrix( iris[1:10, 1:4] )
as.matrix( iris[-c(1:10), 1:4] )
dista(xnew, x)
as.matrix( dist( rbind(xnew, x) ) )
b[ 1:10, -c(1:10) ]
abs(a - b) )
## see the time
x <- matrix( rnorm(1000 * 4), ncol = 4 )
system.time( dista(xnew, x) )
system.time( as.matrix( dist( rbind(xnew, x) ) ) )
x<-b<-a<-xnew<-NULL
Distance correlation
Distance correlation
Description
Distance correlation.
Usage
dcor(x, y)
bcdcor(x, y)
Arguments
x
A numerical matrix.
y
A numerical matrix.
Details
The distance correlation or the bias corrected distance correlation of two matrices is calculated. The
latter one is used for the hypothesis test that the distance correlation is zero (see dcor.ttest).
66
Distance matrix
Value
The value of the distance correlation of the bias corrected distance correlation.
Author(s)
Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
G.J. Szekely, M.L. Rizzo and N. K. Bakirov (2007). Measuring and Testing Independence by
Correlation of Distances. Annals of Statistics, 35(6):2769-2794.
See Also
dcov, dcor.ttest, edist
Examples
x <- as.matrix(iris[1:50, 1:4])
y <- as.matrix(iris[51:100, 1:4])
dcor(x, y)
bcdcor(x, y)
x<-y<-NULL
Distance matrix
Distance matrix
Description
Distance matrix.
Usage
Dist(x, method = "euclidean", square = FALSE, p = 0,vector = FALSE)
vecdist(x)
Arguments
x
A matrix with data. The distances will be calculated between pairs of rows. In
the case of vecdist this is a vector.
method
This is either "euclidean", "manhattan", "canberra1", "canberra2", "minimum",
"maximum", "minkowski","bhattacharyya", "hellinger", "total_variation" or "kullback_leibler/jensen_shannon". The last two options are basically the same.
Distance variance and covariance
67
square
If you choose "euclidean" or "hellinger" as the method, then you can have the option to return the squared Euclidean distances by setting this argument to TRUE.
p
This is for the the Minkowski, the power of the metric.
vector
For return a vector instead a matrix.
Details
The distance matrix is computer with an extra argument for the Euclidean distances.
Value
A square matrix with the pairwise distances.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
References
Mardia K. V., Kent J. T. and Bibby J. M. (1979). Multivariate Analysis. Academic Press.
See Also
dista, colMedians
Examples
x <- matrix(rnorm(50 * 10), ncol = 10)
a1 <- Dist(x)
a2 <- as.matrix( dist(x) )
x<-a1<-a2<-NULL
Distance variance and covariance
Distance variance and covariance
Description
Distance variance and covariances.
Usage
dvar(x)
dcov(x, y)
68
Eigenvalues and eigenvectors in high dimensional principal component analysis
Arguments
x
A numerical matrix.
y
A numerical matrix.
Details
The distance variance of a matrix or the distance covariance of two matrices is calculated.
Value
The distance covariance or distance variance.
Author(s)
Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
G.J. Szekely, M.L. Rizzo and N. K. Bakirov (2007). Measuring and Testing Independence by
Correlation of Distances. Annals of Statistics, 35(6):2769-2794.
See Also
dcor, edist
Examples
x <- as.matrix(iris[1:50, 1:4])
y <- as.matrix(iris[51:100, 1:4])
dcov(x, y)
dvar(x)
Eigenvalues and eigenvectors in high dimensional principal component analysis
Eigenvalues in high dimensional principal component analysis
Description
Eigenvalues in high dimensional (n«p) principal component analysis.
Usage
hd.eigen(x, center = TRUE, scale = FALSE, k = NULL, vectors = FALSE)
Eigenvalues and eigenvectors in high dimensional principal component analysis
69
Arguments
x
A numerical n × p matrix with data where the rows are the observations and the
columns are the variables.
center
Do you want your data centered? TRUE or FALSE.
scale
Do you want each of your variables scaled, i.e. to have unit variance? TRUE or
FALSE.
k
If you want a specific number of eigenvalues and eigenvectors set it here, otherwise all eigenvalues (and eigenvectors if requested) will be returned.
vectors
Do you want the eigenvectors be returned? By dafault this is FALSE.
Details
When n«p, at most the first n eigenvalues are non zero. Hence, there is no need to calculate the
other p-n zero eigenvalues. When center is TRUE, the eigenvalues of the covariance matrix are
calculated. When both the center and scale is TRUE the eigenvalues of the correlation matrix are
calculated. One or more eigenvectors (towards the end) will be 0. In general the signs might be the
opposite than R’s, but this makes no difference.
Value
A list including:
values
A vector with the n (or first k) eigenvalues. The divisor in the crossproduc matrix
is n-1 and not n.
vectors
A matrix of p × n or p × k eigenvectors.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>.
See Also
rmdp
Examples
x <- matrnorm( 40, 100)
a <- hd.eigen(x, FALSE, FALSE)
b <- prcomp(x, center = FALSE, scale = FALSE)
a
b$sdev^2
x <- NULL
70
Energy distance between matrices
Energy distance between matrices
Energy distance between matrices
Description
Energy distance between matrices.
Usage
edist(x, y=NULL)
Arguments
x
A matrix with numbers or a list with matrices.
y
A second matrix with data. The number of comlumns of this matrix must be the
same with the matrix x. The number of rows can be different.
Details
This calculates the energy distance between two matrices. It will work even for tens of thousands
of rows, it will just take some time. See the references for more information. If you have many
matrices and want to calculate the distance matrix, then put them in a list and use eDist.
Value
If "x" is matrix, a numerical value, the energy distance. If "x" is list, a matrix with all pairwsie
distances of the matrices.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
References
Szekely G. J. and Rizzo M. L. (2004) Testing for Equal Distributions in High Dimension, InterStat,
November (5).
Szekely G. J. (2000) Technical Report 03-05, E-statistics: Energy of Statistical Samples, Department of Mathematics and Statistics, Bowling Green State University.
Sejdinovic D., Sriperumbudur B., Gretton A. and Fukumizu, K. (2013). Equivalence of distancebased and RKHS-based statistics in hypothesis testing. The Annals of Statistics, 41(5), 2263-2291.
See Also
dvar, total.dist, total.dista, Dist, dista
71
Equality of objects
Examples
x <- as.matrix( iris[1:50, 1:4] )
y <- as.matrix( iris[51:100, 1:4] )
edist(x, y)
z <- as.matrix(iris[101:150, 1:4])
a <- list()
a[[ 1 ]] <- x
a[[ 2 ]] <- y
a[[ 3 ]] <- z
edist(a)
x<-y<-z<-a<-NULL
Equality of objects
Equality of objects
Description
Equality of objects.
Usage
all_equals(x,y,round_digits = FALSE,without_attr=FALSE,fast_result=FALSE)
Arguments
x
A Matrix, List, Dataframe or Vector.
y
A Matrix, List, Dataframe or Vector.
round_digits
The digit for rounding numbers.
without_attr
A boolean value (TRUE/FALSE) for deleting attributes. Be carefull although
because some atributes are very important for you item.
fast_result
A boolean value (TRUE/FALSE) for using just identical.But you can combine
only with round_digits argument.
Value
A boolean (TRUE/FALSE) value which represents if the items x and y are equal.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
Match, mvbetas, correls, univglms, colsums, colVars
72
Estimation of an AR(1) model
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
y <- matrix( rnorm(100 * 100), ncol = 100 )
all_equals(x,y)
all_equals(x, x)
Estimation of an AR(1) model
Estimation of an AR(1) model
Description
Estimation of an AR(1) model.
Usage
ar1(y, method = "cmle")
colar1(y, method = "cmle")
Arguments
y
For the case of ar1 this is a vector of time series. For the case of colar1 this is a
matrix where weach column represents a time series.
method
This can be either "cmle" for conditional maximum likelihood or "yw" for the
Yule-Walker equations.
Details
Instead of the classical MLE for the AR(1) model which requires numerical optimsation (NewtonRaphson for example) we estimate the parameters of the AR(1) model using conditional maximum
likelihood. This procedure is described in Chapter 17 in Lee (2006). In some, it assumes that the
first observation is deterministic and hence conditioning on that observation, there is a closed form
solution for the parameters. The second alternative is to use the method of moments and hence the
Yule-Walker equations.
Value
param
For the case of ar1 this is a vector with three elements, the constant term, the
φ term (lag coefficient) and the variance. For the case of colar1 this is a matrix
with three columns, eahc of which carries the same aforementioned elements.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Estimation of the Box-Cox transformation
References
http://econ.nsysu.edu.tw/ezfiles/124/1124/img/Chapter17_MaximumLikelihoodEstimation.pdf
See Also
rm.lines, varcomps.mle, rm.anovas
Examples
y <- as.vector(lh)
ar1(y)
ar(y, FALSE, 1, "ols")
ar1(y, method = "yw")
ar(y, FALSE, 1, "yw")
a1 <- colar1(cbind(y, y) )
b1 <- colar1(cbind(y, y), method = "yw")
Estimation of the Box-Cox transformation
Estimation of the Box-Cox transformation
Description
Estimation of the Box-Cox transformation.
Usage
bc(x, low = -1, up = 1)
Arguments
x
A numerical vector with strictly positive values.
low
The lowest value to search for the best λ parameter.
up
The highest value to search for the best λ parameter.
Details
The functions estimates the best λ in the Box-Cox power transformation.
Value
The optimal value of λ.
73
74
Exponential empirical likelihood for a one sample mean vector hypothesis testing
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Box George E. P. and Cox D. R. (1964). An analysis of transformations. Journal of the Royal
Statistical Society, Series B, 26 (2):211-252.
See Also
correls, auc
Examples
x <- exp(rnorm(1000))
bc(x)
Exponential empirical likelihood for a one sample mean vector hypothesis testing
Exponential empirical likelihood for a one sample mean vector hypothesis testing
Description
Exponential empirical likelihood for a one sample mean vector hypothesis testing.
Usage
mv.eeltest1(x, mu, tol = 1e-06, R = 1)
Arguments
x
A matrix containing Euclidean data.
mu
The hypothesized mean vector.
tol
The tolerance value used to stop the Newton-Raphson algorithm.
R
The number of bootstrap samples used to calculate the p-value. If R = 1 (default
value), no bootstrap calibration is performed
Details
Multivariate hypothesis test for a one sample mean vector. This is a non parametric test and it
works for univariate and multivariate data. The p-value is currently computed only asymptotically
(no bootstrap calibration at the moment).
Exponential empirical likelihood hypothesis testing for two mean vectors
75
Value
A list including:
p
The estimated probabiities.
lambda
The value of the Lagrangian parameter λ.
iters
The number of iterations required by the newton-Raphson algorithm.
info
The value of the log-likelihood ratio test statistic along with its corresponding
p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>
References
Jing Bing-Yi and Andrew TA Wood (1996). Exponential empirical likelihood is not Bartlett correctable. Annals of Statistics 24(1): 365-369.
Owen A. B. (2001). Empirical likelihood. Chapman and Hall/CRC Press.
See Also
james, mv.eeltest2
Examples
x <- Rfast::rmvnorm(100, numeric(10), diag( rexp(10, 0.5) ) )
mv.eeltest1(x, numeric(10) )
Exponential empirical likelihood hypothesis testing for two mean vectors
Exponential empirical likelihood hypothesis testing for two mean vectors
Description
Exponential empirical likelihood hypothesis testing for two mean vectors.
Usage
mv.eeltest2(y1, y2, tol = 1e-07, R = 0)
76
Exponential empirical likelihood hypothesis testing for two mean vectors
Arguments
y1
A matrix containing the Euclidean data of the first group.
y2
A matrix containing the Euclidean data of the second group.
tol
The tolerance level used to terminate the Newton-Raphson algorithm.
R
If R is 0, the classical chi-sqaure distribution is used, if R = 1, the corrected chisqaure distribution (James, 1954) is used and if R = 2, the modified F distribution
(Krishnamoorthy and Yanping, 2006) is used. If R is greater than 3 bootstrap
calibration is performed.
Details
Exponential empirical likelihood is a non parametric hypothesis testing procedure for one sample.
The generalisation to two (or more samples) is via searching for the mean vector that minimises the
sum of the two test statistics.
Value
A list including:
test
The empirical likelihood test statistic value.
modif.test
The modified test statistic, either via the chi-square or the F distribution.
pvalue
The p-value.
iters
The number of iterations required by the newton-Raphson algorithm.
mu
The estimated common mean vector.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>
References
Jing Bing-Yi and Andrew TA Wood (1996). Exponential empirical likelihood is not Bartlett correctable. Annals of Statistics 24(1): 365-369.
G.S. James (1954). Tests of Linear Hypothese in Univariate and Multivariate Analysis when the
Ratios of the Population Variances are Unknown. Biometrika, 41(1/2): 19-43.
Krishnamoorthy K. and Yanping Xia (2006). On Selecting Tests for Equality of Two Normal Mean
Vectors. Multivariate Behavioral Research 41(4): 533-548.
Owen A. B. (2001). Empirical likelihood. Chapman and Hall/CRC Press.
Amaral G.J.A., Dryden I.L. and Wood A.T.A. (2007). Pivotal bootstrap methods for k-sample
problems in directional statistics and shape analysis. Journal of the American Statistical Association
102(478): 695-707.
Preston S.P. and Wood A.T.A. (2010). Two-Sample Bootstrap Hypothesis Tests for Three-Dimensional
Labelled Landmark Data. Scandinavian Journal of Statistics 37(4): 568-587.
FBED variable selection method using the correlation
77
Tsagris M., Preston S. and Wood A.T.A. (2017). Nonparametric hypothesis testing for equality of
means on the simplex. Journal of Statistical Computation and Simulation, 87(2): 406-422.
See Also
james, mv.eeltest1
Examples
mv.eeltest2( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]), R = 0 )
mv.eeltest2( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]), R = 1 )
FBED variable selection method using the correlation
FBED variable selection method using the correlation
Description
FBED variable selection method using the correlation.
Usage
cor.fbed(y, x, alpha = 0.05, K = 0)
Arguments
y
The response variable, a numeric vector.
x
A matrix with the data, where the rows denote the samples and the columns are
the variables.
alpha
The significance level, set to 0.05 by default.
K
The number of times to repeat the process. The default value is 0.
Details
FBED stands for Forward Backward with Earcly Dropping. It is a variation of the classical forward
selection, where at each step, only the statistically significant variables carry on. The rest are
dropped. The process stops when no other variables can be selected. If K = 1, the process is
repeated testing sequentially again all those that have not been selected. If K > 1, then this is
repeated.
In the end, the backward selection is performed to remove any falsely included variables. This
backward phase has not been implemented yet.
78
Find element
Value
A list including:
runtime
The duration of the process.
res
A matrix with the index of the selected variable, their test statistic value and the
associated p-value.
info
A matrix with two columns. The cumulative number of variables selected and
the number of tests for each value of K.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Giorgos Borboudakis and Ioannis Tsamardinos (2017). Forward-Backward Selection with Early
Dropping. Arxiv preprint: https://arxiv.org/pdf/1705.10770.pdf
See Also
cor.fsreg, ompr, correls, fs.reg
Examples
x
y
a
a
x
<- matrnorm(100, 100)
<- rnorm(100)
<- cor.fbed(y, x)
<- NULL
Find element
Find element
Description
Search a value in an unordered vector.
Usage
is_element(x, key)
Arguments
x
A vector or matrix with the data.
key
A value to check if exists in the vector x.
Find the given value in a hash table
79
Details
Find if the key exists in the vector and return returns TRUE/FALSE if the value is been found. If
the vector is unordered it is fast but if the vector is ordered then use binary_search. The functions
is written in C++ in order to be as fast as possible.
Value
TRUE/FALSE if the value is been found.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
binary_search (buit-in R function)
Examples
x <- rnorm(500)
key <- x[50]
b <- is_element(x, key)
Find the given value in a hash table
Find the given value in a hash table
Description
Find the given value in a hash table or list.
Usage
hash.find(x,key)
Arguments
x
A hash table or list.
key
The key for searching the table.
Details
This function search the given key.
Value
If the given key exists return its value else returns 0.
80
Fitted probabilities of the Terry-Bradley model
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
See Also
hash.list
Examples
x <- hash.list(letters,c(1:26))
value <- hash.find(x,"a")
x[["a"]]==value
Fitted probabilities of the Terry-Bradley model
Fitted probabilities of the Terry-Bradley model
Description
Fitted probabilities of the Terry-Bradley model.
Usage
btmprobs(x, tol = 1e-09)
Arguments
x
A numerical square, usually not symmetric, matrix with discrete valued data.
Each entry is a frequency, to give an example, the number of wins. x[i, j] is the
number of wins of home team i against guest team j. x[j, i] is the number of
wins of home team j against guest team i.
tol
The tolerance level to terminate the iterative algorithm.
Details
It fits a Bradley-Terry model to the given matrix and returns the fitted probabilities only.
Value
A list including:
iters
The numbetr of iterations required.
probs
A vector with probabilities which sum to 1. This is the probability of win for
each item (or team in our hypothetical example).
Fitting a Dirichlet distribution via Newton-Rapshon
81
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Bradley R.A. and Terry M.E. (1952). Rank Analysis of Incomplete Block Designs: I. The Method
of Paired Comparisons. Biometrika, 39(3/4):324-345.
Huang Tzu-Kuo, Ruby C. Weng and Chih-Jen Lin (2006). Generalized Bradley-Terry models and
multi-class probability estimates. Journal of Machine Learning Research, 7:85-115.
Agresti A. (2002). Categorical Data Analysis (2nd ed). New York: Wiley.
See Also
g2tests, poisson.anova, anova, poisson_only, poisson.mle
Examples
x <- matrix( rpois(10 * 10, 10), ncol = 10) ## not the best example though
btmprobs(x)
Fitting a Dirichlet distribution via Newton-Rapshon
Fitting a Dirichlet distribution via Newton-Rapshon
Description
Fitting a Dirichlet distribution via Newton-Rapshon.
Usage
diri.nr2(x, type = 1, tol = 1e-07)
Arguments
x
A matrix containing the compositional data. Zeros are not allowed.
type
Type 1 uses a vectorised version of the Newton-Raphson (Minka, 2012). In
high dimensions this is to be preferred. If the data are too concentrated, regardless of the dimensions, this is also to be preferrred. Type 2 uses the regular
Newton-Raphson, with matrix multiplications. In small dimensions this can be
considerably faster.
tol
The tolerance level idicating no further increase in the log-likelihood.
82
Floyd-Warshall algorithm
Details
Maximum likelihood estimation of the parameters of a Dirichlet distribution is performed via
Newton-Raphson. Initial values suggested by Minka (2012) are used.
Value
A list including:
loglik
The value of the log-likelihood.
param
The estimated parameters.
Author(s)
Michail Tsagris and Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
References
Minka Thomas (2012). Estimating a Dirichlet distribution. Technical report.
Ng Kai Wang, Guo-Liang Tian, and Man-Lai Tang (2011). Dirichlet and related distributions:
Theory, methods and applications. John Wiley & Sons.
See Also
beta.mle
Examples
x <- matrix( rgamma(100 * 4, c(5, 6, 7, 8), 1), ncol = 4)
x <- x / rowsums(x)
diri.nr2(x)
Floyd-Warshall algorithm
Floyd-Warshall algorithm for shortest paths in a directed graph
Description
Floyd-Warshall algorithm for shortest paths in a directed graph.
Usage
floyd(x)
Floyd-Warshall algorithm
83
Arguments
x
The adjacency matrix of a directed graph. A positive number (including) in x[i,
j] indicates that there is an arrow from i to j and it also shows the cost of going
from i to j. Hence, the algorithm will find not only the shortest path but also the
with the smallest cost. A value of NA means that there is no path. Put positive
number only, as negative will cause problems.
Details
The Floyd-Warshall algorithm is designed to find the shortest path (if it exists) between two nodes
in a graph.
Value
A matrix, say z, with 0 and positive numbers. The elements denote the length of the shortest path
between each pair of points. If z[i, j] is zero it means that there is no cost from i to j. If z[i, j] has a
positive value it means that the length of going from i to j is equal to that value.
Author(s)
John Burkardt (C++ code)
Ported into R and documentation: Manos Papadakis <papadakm95@gmail.com>.
References
Floyd, Robert W. (1962). Algorithm 97: Shortest Path. Communications of the ACM. 5(6): 345.
Warshall, Stephen (1962). A theorem on Boolean matrices. Journal of the ACM. 9 (1): 11-12.
https://en.wikipedia.org/wiki/Floyd
See Also
sort_mat
Examples
x <- matrix(NA, 10, 10)
x[sample(1:100, 10)] <- rpois(10, 3)
floyd(x)
84
Forward selection with generalised linear regression models
Forward selection with generalised linear regression models
Variable selection in generalised linear regression models with forward selection
Description
Variable selection in generalised linear regression models with forward selection
Usage
fs.reg(y, ds, sig = 0.05, tol = 2, type = "logistic")
Arguments
y
ds
sig
tol
type
The dependent variable. This can either be a binary numeric (0, 1) or a vector
with integers (numeric or integer class), count data. The first case is for the
binary logistic regression and the second for the Poisson regression.
The dataset; provide a matrix where columns denote the variables and the rows
the observations. The variables must be continuous, no categorical variables are
accepted.
Significance level for assessing the p-values significance. Default value is 0.05.
The difference bewtween two successive values of the stopping rule. By default
this is is set to 2. If for example, the BIC difference between two succesive models is less than 2, the process stops and the last variable, even though significant
does not enter the model.
If you have a binary dependent variable, put "logistic" or "quasibinomial". If
you have percentages, values between 0 and 1, including 0 and or 1, use "quasibinomial" as well. If you have count data put "poisson".
Details
The classical forward regression is implemented. The difference is that we have an extra step of
check. Even if a variable is significant, the BIC of the model (with that variable) is calculated. If the
decrease from the previous BIC (of the model without this variable) is less thatn a prespecified by
the user value (default is 2) the variable wil enter. This way, we guard somehow against over-fitting.
Value
A matrix with for columns, the selected variables, the logarithm of their p-value, their test statistic
and the BIC of the model with these variables included. If no variable is selected, the matrix is
empty.
Author(s)
Marios Dimitriadis
Documentation: Marios Dimitriadis <kmdimitriadis@gmail.com>.
G-square test of conditional indepdence
85
See Also
cor.fsreg, logistic_only, poisson_only, glm_logistic, glm_poisson
Examples
set.seed(123)
#simulate a dataset with continuous data
x <- matrnorm(100, 50)
y <- rpois(100, 10)
a <- fs.reg(y, x, sig = 0.05, tol = 2, type = "poisson")
y <- rbinom(100, 1, 0.5)
b <- fs.reg(y, x, sig = 0.05, tol = 2, type = "logistic")
x <- NULL
G-square test of conditional indepdence
G-square test of conditional indepdence
Description
G-square test of conditional indepdence with and without permutations.
Usage
g2Test(data, x, y, cs, dc)
g2Test_perm(data, x, y, cs, dc, nperm)
Arguments
data
A numerical matrix with the data. The minimum must be 0, otherwise the
function can crash or will produce wrong results.
x
A number between 1 and the number of columns of data. This indicates which
variable to take.
y
A number between 1 and the number of columns of data (other than x). This
indicates the other variable whose independence with x is to be tested.
cs
A vector with the indices of the variables to condition upon. It must be non
zero and between 1 and the number of variables. If you want unconditional
independence test see g2Test_univariate and g2Test_univariate_perm. If
there is an overlap between x, y and cs you will get 0 as the value of the test
statistic.
dc
A numerical value equal to the number of variables (or columns of the data matrix) indicating the number of distinct, unique values (or levels) of each variable.
Make sure you give the correct numbers here, otherwise the degrees of freedom
will be wrong.
86
G-square test of conditional indepdence
nperm
The number of permutations. The permutations test is slower than without permutations and should be used with small sample sizes or when the contigency
tables have zeros. When there are few variables, R’s "chisq.test" function is
faster, but as the number of variables increase the time difference with R’s procedure becomes larger and larger.
Details
The functions calculates the test statistic of the G2 test of conditional independence between x and
y conditional on a set of variable(s) cs.
Value
A list including:
statistic
The G2 test statistic.
df
The degrees of freedom of the test statistic.
x
The row or variable of the data.
y
The column or variable of the data.
Author(s)
Giorgos Borboudakis. The permutation version used a C++ code by John Burkardt.
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
References
Tsamardinos, I., & Borboudakis, G. (2010). Permutation testing improves Bayesian network learning. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases
(pp. 322-337). Springer Berlin Heidelberg
See Also
g2Test_univariate, g2Test_univariate_perm, correls, univglms
Examples
nvalues <- 3
nvars <- 10
nsamples <- 5000
data <- matrix( sample( 0:(nvalues - 1), nvars * nsamples, replace = TRUE ), nsamples, nvars )
dc <- rep(nvalues, nvars)
g2Test( data, 1, 2, 3, c(3, 3, 3) )
g2Test_perm( data, 1, 2, 3, c(3, 3, 3), 1000 )
dc<-data<-NULL
Gaussian regression with a log-link
Gaussian regression with a log-link
Gaussian regression with a log-link
Description
Gaussian regression with a log-link.
Usage
normlog.reg(y, x, tol = 1e-07, maxiters = 100)
Arguments
y
The dependent variable, a numerical variable with non negative numbers.
x
A matrix or data.frame with the indendent variables.
tol
The tolerance value to terminate the Newton-Raphson algorithm.
maxiters
The maximum number of iterations that can take place in the regression.
Details
A Gaussian regression with a log-link is fitted.
Value
A list including:
i
The number of iterations required by the Newton-Raphson
loglik
The log-likelihood value.
deviance
The deviance value.
be
The regression coefficients
Author(s)
Stefanos Fafalios
R implementation and documentation: Stefanos Fafalios <stefanosfafalios@gmail.com>
See Also
normlog.regs, score.glms, prop.regs, allbetas
87
88
Generates random values from a normal and puts them in a matrix
Examples
y <- abs( rnorm(100) )
x <- matrix( rnorm(100 * 2), ncol = 2)
a <- normlog.reg(y, x)
b <- glm(y ~ x, family = gaussian(log) )
summary(b)
a
Generates random values from a normal and puts them in a matrix
Generates random values from a normal and puts them in a matrix
Description
Generates random values from a normal and puts them in a matrix.
Usage
matrnorm(n, p)
Arguments
n
The sample size, the number of rows the matrix will have.
p
The dimensionality of the data, the nubmer of columns of the matrix.
Details
How many times did you have to simulated data from a (standard) normal distribution in order to
test something? For example, in order to see the speed of logistic_only, one needs to generate
a matrix with predictor variables. The same is true for other similar functions. In sftests, one
would like to examine the typer I error of this test under the null hypothesis.
By using the Ziggurat method of generating standard normal variates, this function is really fast
when you want to generate big matrices.
Value
An n x p matrix with data simulated from a standard normal distribution.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
See Also
rvmf, Rnorm, rmvnorm, rvonmises
Get specific columns/rows fo a matrix
Examples
x <- matrnorm(100, 100)
Get specific columns/rows fo a matrix
Get specific columns/rows fo a matrix
Description
Get specific columns/rows of a matrix.
Usage
columns(x,indices)
rows(x,indices)
Arguments
x
A matrix with data.
indices
An integer vector with the indices.
Value
A matrix with the specific columns/rows of argumment indices.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, rowFalse, nth, colrange, colMedians, colVars, sort_mat, rowTrue
Examples
x <- matrix(runif(100*100),100,100)
indices = sample(1:100,50)
all.equal(x[,indices],columns(x,indices))
all.equal(x[indices,],rows(x,indices))
x<-indices<-NULL
89
90
Hash - Pair function
Hash - Pair function
Hash - Pair function
Description
Hash - Pair function.
Usage
hash.list(key,x)
Arguments
key
The keys of the given values.
x
The values.
Details
This function pairs each item of of key and value make a unique hash table.
Value
Returns the hash-list table.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
See Also
hash.find
Examples
x <- hash.list(letters,c(1:26))
x[["a"]]==1
Hash object to a list object
91
Hash object to a list object
Hash object to a list object
Description
Hash object to a list object.
Usage
hash2list(x, sorting = FALSE)
Arguments
x
A hash table with two parts, the keys (number(s) as string) and the key values (a
single number).
sorting
This is if you you want the numbers in the keys sorted. The default value is
FALSE.
Details
For every key, there is a key value. This function creates a list and puts every pair of keys and value
in a component of a list.
Value
A list whose length is equal to the size of the hash table.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
hash.list, hash.find
Examples
x=list("1 2 4 3"=2.56,"2.34 1.05"=2)
hash2list(x)
hash2list(x,TRUE)
92
High dimensional MCD based detection of outliers
High dimensional MCD based detection of outliers
High dimensional MCD based detection of outliers
Description
High dimensional MCD based detection of outliers.
Usage
rmdp(y, alpha = 0.05, itertime = 100)
Arguments
y
A matrix with numerical data with more columns (p) than rows (n), i.e. n<p.
alpha
The significance level, i.e. used to decide whether an observation is said to be
considered a possible outlier. The default value is 0.05.
itertime
The number of iterations the algorithm will be ran. The higher the sample size,
the larger this number must be. With 50 observations in R1 000 maybe this has
to be 1000 in order to produce stable results.
Details
High dimensional outliers (n«p) are detected using a properly constructed MCD. The variances of
the variables are used and the determinant is simply their product.
Value
A list including: runtime = runtime, dis = dis, wei = wei
runtime
The duration of the process.
dis
The final estimated Mahalanobis type normalised distances.
wei
A bollean variable vector specifying whether an observation is "clean" (TRUE)
or a possible outlier (FALSE).
cova
The estimated covatriance matrix.
Author(s)
Initial R code: Changliang Zou <nk.chlzou@gmail.com> R code modifications: Michail Tsagris
<mtsagris@yahoo.gr> C++ implementation: Manos Papadakis <papadakm95@gmail.com> Documentation: Michail Tsagris <mtsagris@yahoo.gr> and Changliang Zhou <nk.chlzou@gmail.com>
References
Ro K., Zou C., Wang Z. and Yin G. (2015). Outlier detection for high-dimensional data. Biometrika,
102(3):589-599.
Hypothesis test for the distance correlation
93
See Also
colmeans, colVars, colMedians
Examples
x <- matrix(rnorm(50 * 400), ncol = 400)
a <- rmdp(x, itertime = 500)
x<-a<-NULL
Hypothesis test for the distance correlation
Hypothesis test for the distance correlation
Description
Hypothesis test for the distance correlation.
Usage
dcor.ttest(x, y, logged = FALSE)
Arguments
x
A numerical matrix.
y
A numerical matrix.
logged
Do you want the logarithm of the p-value to be returned? If yes, set this to
TRUE.
Details
The bias corrected distance correlation is used. The hypothesis test is whether the two matrices are
independent or not. Note, that this test is size correct as both the sample size and the dimensionality
goes to infinity. It will not have the correct type I error for univariate data or for matrices with just
a couple of variables.
Value
A vector with 4 elements, the bias corrected distance correlation, the degrees of freedom, the test
statistic and its associated p-value.
Author(s)
Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
94
Hypothesis test for two means of percentages
References
G.J. Szekely, M.L. Rizzo and N. K. Bakirov (2007). Measuring and Testing Independence by
Correlation of Distances. Annals of Statistics, 35(6):2769-2794.
See Also
bcdcor, dcov, edist
Examples
x <- as.matrix(iris[1:50, 1:4])
y <- as.matrix(iris[51:100, 1:4])
dcor.ttest(x, y)
Hypothesis test for two means of percentages
Hypothesis test for two means of percentages
Description
Hypothesis test for two means of percentages.
Usage
percent.ttest(x, y, logged = FALSE)
Arguments
x
A numerical vector with the percentages of the first sample. Any value between
0 and 1 (inclusive) is allowed.
y
A numerical vector with the percentages of the first sample. Any value between
0 and 1 (inclusive) is allowed.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
This is the prop.reg but with a single categorical predictor which has two levels only. It is like a
t-test for the means of two samples haivng percentages.
Value
A vector with three elements, the phi parameter, the test statistic and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Hypothesis test for von Mises-Fisher distribution over Kent distribution
95
References
Papke L. E. & Wooldridge J. (1996). Econometric methods for fractional response variables with
an application to 401(K) plan participation rates. Journal of Applied Econometrics, 11(6): 619-632.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
link{percent.ttests}, prop.reg, ttest2, ftest
Examples
x <- rbeta(100, 3, 1)
y <- rbeta(100, 7.5, 2.5)
percent.ttest(x, y)
Hypothesis test for von Mises-Fisher distribution over Kent distribution
Hypothesis test for von Mises-Fisher distribution over Kent distribution
Description
The null hypothesis is whether a von Mises-Fisher distribution fits the data well, and the altenrative
is that the Kent distribution is more suitable.
Usage
fish.kent(x, logged = FALSE)
Arguments
x
A numeric matrix containing the data as unit vectors in Euclidean coordinates.
logged
If you want the logarithm of the p-value ot be returned set this to TRUE.
Details
Essentially it is a test of rotational symmetry, whether Kent’s ovalness parameter (beta) is equal to
zero. This works for spherical data only.
Value
A vector with two elements, the value of the test statistic and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
96
Hypothesis testing betseen two skewness or kurtosis coefficients
References
Rivest, L. P. (1986). Modified Kent’s statistics for testing goodness of fit for the Fisher distribution
in small concentrated samples. Statistics & probability letters, 4(1): 1-4.
See Also
vmf.mle, iag.mle
Examples
x <- rvmf(100, rnorm(3), 15)
fish.kent(x)
x <- NULL
Hypothesis testing betseen two skewness or kurtosis coefficients
Skewness and kurtosis coefficients
Description
Skewness and kurtosis coefficients.
Usage
skew.test2(x, y)
kurt.test2(x, y)
Arguments
x
A numerical vector with data.
y
A numerical vector with data, not necessarily of the same size.
Details
The skewness of kurtosis coefficients between two samples are being compared.
Value
A vector with the test statistic and its associated p-value.
Author(s)
Klio Lakiotaki
R implementation and documentation: Klio Lakiotaki <kliolak@gmail.com>.
Index of the columns of a data.frame which are factor variables
97
References
https://en.wikipedia.org/wiki/Skewness
https://en.wikipedia.org/wiki/Kurtosis
See Also
skew, colskewness, colmeans, colVars, colMedians
Examples
x <- rgamma(150,1, 4)
y <- rgamma(100, 1, 4)
skew.test2(x, y)
kurt.test2(x, y)
Index of the columns of a data.frame which are factor variables
Index of the columns of a data.frame which are factor variables
Description
Index of the columns of a data.frame which are factor variables.
Usage
which_isFactor(x)
Arguments
A data.frame where some columns are expected to be factor variables.
x
Details
The function is written in C++ and this is why it is very fast.
Value
A vector with the column indices which are factor variables. If there are no factor variables it will
return an empty vector.
Author(s)
Manos Papadakis <papadakm95@gmail.com>
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
nth, Match
98
Insert new function names in the NAMESPACE file
Examples
which_isFactor(iris)
Insert new function names in the NAMESPACE file
Insert new function names in the NAMESPACE file
Description
Insert new function names in the NAMESPACE file.
Usage
AddToNamespace(path.namespace,path.rfolder,sort = FALSE)
Arguments
path.namespace An full path to the NAMESPACE file.
path.rfolder
An full path to the directory the new files to be added are stored.
sort
An boolean value for sorting the exported functions in file NAMESPACE.
Details
Reads the files that are exported in NAMESPACE and the files inside rfolder (where R files are) and
insert every file that is not exported. To work properly must each R file to have the same name with
the exported function. Also every file must have only one function.
Value
Returns the file that added in the export or empty character vector if all the files was inserted.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colShuffle, colVars, colmeans, read.directory
Inverse of a symmetric positive definite matrix
99
Examples
## Not run:
# for example: path.namespace="C:\some_file\NAMESPACE" where is NAMESPACE file
# path.rfolder="C:\some_file\R\" where is R files are
# system.time( a<-AddToNamespace(path.namespace,path.rfolder) )
# if(length(a)==0){
# print("all the files are inserted")
# }else{
# print("The new files that inserted are: \n")
# a
# }
## End(Not run)
Inverse of a symmetric positive definite matrix
Inverse of a symmetric positive definite matrix
Description
Inverse of a symmetric positive definite matrix.
Usage
spdinv(A)
Arguments
A
A square positive definite matrix.
Details
After calculating the Cholesky decomposition of the matrix we use this upper triangular matrix to
invert the original matrix.
Value
The inverse of the input matrix.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
http://econ.nsysu.edu.tw/ezfiles/124/1124/img/Chapter17_MaximumLikelihoodEstimation.pdf
100
James multivariate version of the t-test
See Also
cholesky, cova
Examples
s <- cova( as.matrix(iris[, 1:4]) )
spdinv(s)
solve(s)
James multivariate version of the t-test
James multivariate version of the t-test
Description
James test for testing the equality of two population mean vectors without assuming equality of the
covariance matrices.
Usage
james(y1, y2, a = 0.05, R = 1)
Arguments
y1
A matrix containing the Euclidean data of the first group.
y2
A matrix containing the Euclidean data of the second group.
a
The significance level, set to 0.05 by default.
R
If R is 1 the classical James test is returned. If R is 2 the MNV modficiation is
implemented.
Details
Multivariate analysis of variance without assuming equality of the covariance matrices. The p-value
can be calculated either asymptotically or via bootstrap. The James test (1954) or a modification
proposed by Krishnamoorthy and Yanping (2006) is implemented. The James test uses a corected
chi-square distribution, whereas the modified version uses an F distribution.
Value
A list including:
note
A message informing the user about the test used.
mesoi
The two mean vectors.
info
The test statistic, the p-value, the correction factor and the corrected critical
value of the chi-square distribution if the James test has been used or, the test
statistic, the p-value, the critical value and the degrees of freedom (numerator
and denominator) of the F distribution if the modified James test has been used.
k nearest neighbours algorithm (k-NN)
101
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>
References
G.S. James (1954). Tests of Linear Hypothese in Univariate and Multivariate Analysis when the
Ratios of the Population Variances are Unknown. Biometrika, 41(1/2): 19-43
Krishnamoorthy K. and Yanping Xia. On Selecting Tests for Equality of Two Normal Mean Vectors
(2006). Multivariate Behavioral Research 41(4): 533-548
See Also
mv.eeltest2
Examples
james( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]), R = 1 )
james( as.matrix(iris[1:25, 1:4]), as.matrix(iris[26:50, 1:4]), R = 2 )
k nearest neighbours algorithm (k-NN)
k nearest neighbours algorithm (k-NN)
Description
k nearest neighbours algorithm (k-NN).
Usage
knn(xnew, y, x, k, dist.type = "euclidean", type = "C", method = "average",
freq.option = 0, mem.eff = FALSE)
Arguments
xnew
The new data, new predictor variable values. A matrix with numerical data.
y
A vector with the response variable, whose values for the new data we wish to
predict. This can be numerical data, factor or discrete, 0, 1, ... The latter two
cases are for classification.
x
The dataset. A matrix with numerical data.
k
The number of nearest neighbours to use. The number can either be a single
value or a vector with multiple values.
dist.type
The type of distance to be used. Either \"euclidean\" or \"manhattan\".
102
k nearest neighbours algorithm (k-NN)
type
If your response variable \"y\" is numerical data, then this should be \"R\" (regression). If \"y\" is in general categorical, factor or discrete set this argument
to \"C\" (classification).
method
In case you have regression (type = \"R\") you want a way to summarise the
prediction. If you want to take the average of the reponses of the k closest
observations, type \"average\". For the median, type \"median\" and for the
harmonic mean, type \"harmonic\".
freq.option
If classification (type = \"C\") and ties occur in the prediction, more than one
class has the same number of k nearest neighbours, in which case there are two
strategies available: Option 0 selects the first most frequent encountered. Option
1 randomly selects the most frequent value, in the case that there are duplicates.
mem.eff
Boolean value indicating a conservative or not use of memory. Lower usage of
memory/Having this option on will lead to a slight decrease in execution speed
and should ideally be on when the amount of memory in demand might be a
concern.
Details
The concept behind k-NN is simple. Suppose we have a matrix with predictor variables and a
vector with the response variable (numerical or categorical). When a new vector with observations
(predictor variables) is available, its corresponding response value, numerical or category is to be
predicted. Instead of using a model, parametric or not, one can use this ad hoc algorithm.
The k smallest distances between the new predictor variables and the existing ones are calculated.
In the case of regression, the average, median or harmonic mean of the corresponding respone
values of these closest predictor values are calculated. In the case of classification, i.e. categorical
response value, a voting rule is applied. The most frequent group (response value) is where the new
observation is to be allocated.
Value
A matrix whose number of columns is equal to the size of k. If in the input you provided there is
just one value of k, then a matrix with one column is returned containing the predicted values. If
more than one value was supplied, the matrix will contain the predicted values for every value of k.
Author(s)
Marios Dimitriadis
R implementation and documentation: Marios Dimitriadis <kmdimitriadis@gmail.com>
References
Cover TM and Hart PE (1967). Nearest neighbor pattern classification. IEEE Transactions on
Information Theory. 13(1):21-27.
Friedman J., Hastie T. and Tibshirani R. (2017). The elements of statistical learning. New York:
Springer.
http://web.stanford.edu/~hastie/ElemStatLearn/printings/ESLII_print12.pdf
http://statlink.tripod.com/id3.html
103
k-NN algorithm using the arc cosinus distance
See Also
logistic_only, fs.reg, cor.fsreg
Examples
# Simulate a dataset with continuous data
x <- as.matrix(iris[, 1:4])
y <- as.numeric(iris[, 5])
id <- sample(1:150, 120)
mod <- knn(x[-id, ], y[id], x[id, ], k = c(4, 5,
mod # Predicted values of y for 3 values of k.
table(mod[, 1], y[-id] ) # Confusion matrix for
table(mod[, 2], y[-id] ) # Confusion matrix for
table(mod[, 3], y[-id] ) # Confusion matrix for
6), type = "C", mem.eff = FALSE)
k = 4
k = 5
k = 6
k-NN algorithm using the arc cosinus distance
k-NN algorithm using the arc cosinus distance
Description
It classifies new observations to some known groups via the k-NN algorithm.
Usage
dirknn(xnew, x, y, k, type = "C", parallel = FALSE)
Arguments
xnew
The new data whose membership is to be predicted, a numeric matrix with unit
vectors.
x
The data, a numeric matrix with unit vectors.
k
The number of nearest neighbours. It can also be a vector with many values.
y
A numerical vector representing the class or label of each vector of x. 1, 2,
3, and so on. It can also be a numerical vector with data in order to perform
regression.
type
If your response variable y is numerical data, then this should be "R" (regression). If y is in general categorical set this argument to "C" (classification).
parallel
Do you want th ecalculations to take place in parallel? The default value is
FALSE.
104
Linear models for large scale data
Details
The standard algorithm is to keep the k nearest observations and see the groups of these observations. The new observation is allocated to the most frequent seen group. The non standard algorithm
is to calculate the classical mean or the harmonic mean of the k nearest observations for each group.
The new observation is allocated to the group with the smallest mean distance.
If you want regression, the predicted value is calculated as the average of the responses of the k
nearest observations.
Value
A matrix with the predicted group(s). It has as many columns as the values of k.
Author(s)
Stefanos Fafalios
R implementation and documentation: Stefanos Fafalios <stefanosfafalios@gmail.com>
See Also
knn, vmf.mle, spml.mle
Examples
x <- as.matrix(iris[, 1:4])
x <- x/sqrt( rowSums(x^2) )
y<- as.numeric( iris[, 5] )
a <- dirknn(x, x, y, k = 2:10)
Linear models for large scale data
Linear models for large scale data
Description
Linear models for large scale data.
Usage
lmfit(x, y, w = NULL)
Arguments
x
y
w
The design matrix with the data, where each column refers to a different sample
of subjects. You must supply the design matrix, with the column of 1s. This
function is the analogue of lm.fit and .lm.fit.
A numerical vector or a numerical matrix.
An optional numerical vector with weights. Note that if you supply this, the
function does not make them sum to 1. So, you should do it.
Logistic and Poisson regression models
105
Details
We have simply exploitted R’s powerful function and managed to do better than .lm.fit which is a
really powerful function as well. This is a bare bones function as it returns only two things, the
coefficients and the residuals. .lm.fit returns more and lm.fit even more and finally lm returns too
much. The motivatrion came form this site https://m-clark.github.io/docs/fastr.html . We changed
the function a bit.
Value
A list including:
be
The beta coefficients.
residuals
The residuals of the linear model(s).
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
See Also
regression, allbetas, correls, mvbetas, cor.fsreg
Examples
n <- 200 ; p <- 5
X <- matrnorm(n, p)
y <- rnorm(200)
a1 <- .lm.fit(X, y)
a2 <- lmfit(X, y)
x <- NULL
Logistic and Poisson regression models
Logistic and Poisson regression models
Description
Logistic and Poisson regression models.
106
Logistic and Poisson regression models
Usage
glm_logistic(x, y, full = FALSE,tol = 1e-09, maxiters = 100)
glm_poisson(x, y, full = FALSE,tol = 1e-09)
Arguments
x
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables. This can be a matrix or a data.frame (with
factors).
y
The dependent variable; a numerical vector with two values (0 and 1) for the
logistic regression or integer values, 0, 1, 2,... for the Poisson regression.
full
If this is FALSE, the coefficients and the deviance will be returned only. If this
is TRUE, more information is returned.
tol
The tolerance value to terminate the Newton-Raphson algorithm.
maxiters
The max number of iterations that can take place in each regression.
Details
The function is written in C++ and this is why it is very fast.
Value
When full is FALSE a list including:
be
The regression coefficients.
devi
The deviance of the model.
When full is TRUE a list including:
info
The regression coefficients, their standard error, their Wald test statistic and their
p-value.
devi
The deviance.
Author(s)
Manos Papadakis <papadakm95@gmail.com>
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
poisson_only, logistic_only, univglms, regression
Logistic or Poisson regression with a single categorical predictor
107
Examples
x <- matrix(rnorm(100 * 3), ncol = 3)
y <- rbinom(100, 1, 0.6)
## binary logistic regression
a1 <- glm_logistic(x, y, full = TRUE)
a2 <- glm(y ~ x, binomial)
x <- matrix(rnorm(100 * 3), ncol = 3)
y <- rpois(100, 10)
## binary logistic regression
b1 <- glm_poisson(x, y, full = TRUE)
b2 <- glm(y ~ x, poisson)
x<-y<-a1<-a2<-b1<-b2<-NULL
Logistic or Poisson regression with a single categorical predictor
Logistic or Poisson regression with a single categorical predictor
Description
Logistic or Poisson regression with a single categorical predictor.
Usage
logistic.cat1(y, x, logged = FALSE)
poisson.cat1(y, x, logged = FALSE)
Arguments
y
x
logged
A numerical vector with values 0 or 1.
A numerical vector with discrete numbers or a factor variable. This is suppose to
be a categorical predictor. If you supply a continuous valued vector the function
will obviously provide wrong results. Note: For the "binomial.anova" if this is
a numerical vector it must contain strictly positive numbers, i.e. 1, 2, 3, 4, ..., no
zeros are allowed.
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
There is a closed form solution for the logistic regression in the case of a single predictor variable.
See the references for more information.
Value
info
devs
res
A matrix similar to the one produced by the glm command. The estimates, their
standard error, the Wald value and the relevant p-value.
For the logistic regression case a vector with the null and the residual deviances,
their difference and the significance of this difference.
For the Poisson regression case a vector with the log likelihood ratio test statistic
value and its significance.
108
Lower and Upper triangular of a matrix
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Stan Lipovetsky (2015). Analytical closed-form solution for binary logit regression by categorical
predictors. Journal of Applied Statistics, 42(1): 37–49.
See Also
poisson.anova, poisson.anovas, anova, logistic_only, poisson_only
Examples
y <- rbinom(20000, 1, 0.6)
x <- as.factor( rbinom(20000, 3, 0.5) )
system.time( a1 <- logistic.cat1(y, x) )
system.time( a2 <- glm(y ~ x, binomial) )
a1 ; a2
y <- rpois(20000, 10)
x <- as.factor( rbinom(20000, 3, 0.5) )
system.time( a1 <- poisson.cat1(y, x) )
system.time( a2 <- glm(y ~ x, poisson) )
a1
; a2
x<-y<-a1<-a2<-NULL
Lower and Upper triangular of a matrix
Lower and Upper triangular of a matrix
Description
Lower/upper triangular matrix.
Usage
lower_tri(x, suma = FALSE, diag = FALSE)
upper_tri(x, suma = FALSE, diag = FALSE)
Lower and Upper triangular of a matrix
109
Arguments
x
A matrix with data or a vector with 2 values which is the dimension of the logical
matrix to be returned with the upper or lower triangular filled with \"TRUE\".
suma
A logical value for returning the sum of the upper or lower triangular. By default
is \"FALSE\". Works only if argument "x" is matrix.
diag
A logical value include the diagonal to the result.
Value
Get a lower/upper triangular logical matrix with values \"TRUE\"/\"FALSE\"" or a vector with the
values of a lower/upper triangular or the sum of the upper/lower triangular if suma is set \"TRUE\".
You can also include diagonal with any operation if argument diag is set to "TRUE".
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, colFalse, nth, rowrange, rowMedians, rowVars, sort_mat, colTrue
Examples
x <- matrix(runif(10*10),10,10)
all.equal(lower_tri(c(10,10)),lower.tri(x))
all.equal(lower_tri(x),x[lower.tri(x)])
#all.equal(upper_tri(c(10,10)),upper.tri(x))
#all.equal(upper_tri(x),x[upper.tri(x)])
#all.equal(lower_tri(c(10,10),diag = TRUE),lower.tri(x,diag = TRUE))
#all.equal(lower_tri(x,diag = TRUE),x[lower.tri(x,diag = TRUE)])
#all.equal(upper_tri(c(10,10),diag = TRUE),upper.tri(x,diag = TRUE))
#all.equal(upper_tri(x,diag = TRUE),x[upper.tri(x,diag = TRUE)])
x<-NULL
110
Mahalanobis distance
Mahalanobis distance
Mahalanobis distance
Description
Mahalanobis distance.
Usage
mahala(x, mu, sigma, ischol = FALSE)
Arguments
x
A matrix with the data, where rows denotes observations (vectors) and the columns
contain the variables.
mu
The mean vector.
sigma
The covariance or any square symmetric matrix.
ischol
A boolean variable set to true if the Cholesky decomposition of the covariance
matrix is supplied in the argument \"sigma\".
Value
A vector with the Mahalanobis distances.
Author(s)
Matteo Fasiolo <matteo.fasiolo@gmail.com>,
C++ and R implementation and documentation: Matteo Fasiolo <matteo.fasiolo@gmail.com>.
See Also
dista, colmeans
Examples
x <- matrix( rnorm(100 * 50), ncol = 50 )
m <- colmeans(x)
s <- cov(x)
a1 <- mahala(x, m, s)
Many (and one) area aunder the curve values
111
Many (and one) area aunder the curve values
Many are aunder the curve values
Description
Many are aunder the curve values.
Usage
colaucs(group, preds)
auc(group, preds)
Arguments
group
A numerical vector with two values, one of which must be strictly 1.
preds
A numerical matrix with scores, probabilities or any other measure. In the case
of auc this is a vector.
Details
The AUCs are calculated column-wise or just an AUC if the vector function is used.
Value
A vector with length equal to the number of columns of the "preds" argument. The AUC vlaues for
each column. If the "auc" function is used then a signle number is returned.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
ttests, ttest, ftests
Examples
## 200 variables, hence 200 AUCs will be calculated
x <- matrix( rnorm(100 * 200), ncol = 200 )
ina <- rbinom(100, 1, 0.6)
system.time( colaucs(ina, x) )
a <- colaucs(ina, x)
b <- auc(ina, x[, 1])
x <- NULL
112
Many 2 sample proportions tests
Many 2 sample proportions tests
Many 2 sample proportions tests
Description
It performs very many 2 sample proportions tests.
Usage
proptests(x1, x2, n1, n2)
Arguments
x1
A vector with the successes of the one group.
x2
A vector with the successes of the one group.
n1
A vector with the number of trials of the one group.
n2
A vector with the number of trials of the one group.
Details
The 2-sample proportions test is performed for each pair of proportions of teh two groups.
Value
A matrix with the proportions of each group (two columns), the test statistic and the p-value of each
test.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
B. L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika,
38(3/4), 330-336.
See Also
ttests, ftests, colVars
113
Many 2 sample tests
Examples
## 10000 variables, hence 10000 t-tests will be performed
set.seed(12345)
x1 <- rpois(500, 5)
x2 <- rpois(500, 5)
n1 <- rpois(1000, 40)
n2 <- rpois(1000, 40)
a <- proptests(x1, x2, n1, n2)
mean(a[, 4]<0.05)
x1 <- rbinom(500, 500, 0.6)
x2 <- rbinom(500, 500, 0.6)
b <- proptests(x1, x2, 500, 500)
mean(b[, 4]<0.05)
Many 2 sample tests
Many 2 sample tests tests
Description
It performs very many 2 sample tests.
Usage
ttests(x, y = NULL, ina, paired = FALSE, logged = FALSE, parallel = FALSE)
mcnemars(x, y = NULL, ina, logged = FALSE)
var2tests(x, y = NULL, ina, alternative = "unequal", logged = FALSE)
Arguments
x
A matrix with the data, where the rows denote the samples and the columns are
the variables.
y
A second matrix with the data of the second group. If this is NULL (default
value) then the argument ina must be supplied. Notice that when you supply the
two matrices the procedure is two times faster.
ina
A numerical vector with 1s and 2s indicating the two groups. Be careful, the
function is designed to accept only these two numbers. In addition, if your "y"
is NULL, you must specify "ina".
alternative
The type of hypothesis to be checked, "equal", "greater", "less".
paired
If the groups are not independent paired t-tests should be performed and this
must be TRUE, otherwise, leave it FALSE. In this case, the two groups must
have equal smaple sizes, otherwise no test will be performed.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
parallel
Should parallel implentations take place in C++? The default value is FALSE.
114
Many analysis of variance tests with a discrete variable
Details
For the ttests, if the groups are independent, the Welch’s t-test (without assuming equal variances)
is performed. Otherwise many paired t-tests are performed. The McNemar’s test requires a number
of observations, at least 30 would be good in order for the test to have some power and be size
corect.
Value
A matrix with the test statistic, the degrees of freedom (if the groups are independent) and the
p-value (or their logarithm) of each test.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
B. L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika,
38(3/4), 330-336. McNemar Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika. 12(2):153-157.
See Also
ftests, anovas, ttest
Examples
## 1000 variables, hence 1000 t-tests will be performed
x = matrnorm(100, 100)
## 100 observations in total
ina = rbinom(100, 1, 0.6) + 1
## independent samples t-test
system.time( ttests(x, ina = ina) )
x1 = x[ina == 1, ]
x2 = x[ina == 2, ]
system.time( ttests(x1, x2) )
x <- NULL
Many analysis of variance tests with a discrete variable
Many analysis of variance tests with a discrete variable
Description
Many analysis of variance tests with a discrete variable.
Many analysis of variance tests with a discrete variable
115
Usage
poisson.anovas(y, ina, logged = FALSE)
quasipoisson.anovas(y, ina, logged = FALSE)
geom.anovas(y, ina, type = 1, logged = FALSE)
Arguments
y
A numerical matrix with discrete valued data, i.e. counts for the case of the
Poisson, or with 0s and 1s for the case of the Bernoulli distribution. Each column
represents a variable.
ina
A numerical vector with discrete numbers starting from 1, i.e. 1, 2, 3, 4,... or
a factor variable. This is suppose to be a categorical predictor. If you supply a
continuous valued vector the function will obviously provide wrong results.
type
This rgument is for the geometric distribution. Type 1 refers to the case where
the minimum is zero and type 2 for the case of the minimum being 1.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
This is the analysis of variance with count data. What we do is many log-likelihood ratio tests. For
the quasi Poisson case we scale the difference in the deviances.
Value
A matrix with two values, the difference in the deviances (test statistic) and the relevant p-value.
For the case of quasi Poisson the estimated φ parameter is also returned.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
g2tests, poisson.anova, anova, poisson_only, poisson.mle
Examples
ina <- rbinom(500, 3, 0.5) + 1
## Poisson example
y <- matrix( rpois(500 * 100, 10), ncol= 100 )
system.time(a1 <- poisson.anovas(y, ina) )
y <- NULL
116
Many ANCOVAs
Many ANCOVAs
Many ANCOVAs
Description
Many ANCOVAs.
Usage
ancovas(y, ina, x, logged = FALSE)
Arguments
y
A matrix with the data, where the rows denote the observations and the columns
are the variables.
ina
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Be
careful, the function is desinged to accept numbers greater than zero.
x
A numerical vector whose length is equal to the number of rows of y. This is the
covariate.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
Many Analysis of covariance tests are performed. No interaction between the factor and the covariate is tested. Only the main effects. The design need not be balanced. The values of ina need
not have the same frequency. The sums of squares have been adjusted to accept balanced and
unbalanced designs.
Value
A matrix with the test statistic and the p-value for the factor variable and the covariate.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
D.C. Montgomery (2001). Design and analysis of experiments (5th Edition). New York: John
Wiley \& Sons
See Also
ftests, ttests, anovas
Many exponential regressions
117
Examples
## 100 variables, hence 100 F-tests will be performed
y <- matrix( rnorm(90 * 100), ncol = 100 )
ina <- rbinom(90, 2, 0.5) + 1
x <- rnorm(90)
system.time( a <- ancovas(y, ina, x) )
m1 <- lm(y[, 15] ~ factor(ina) + x)
m2 <- lm(y[, 15] ~ x + factor(ina))
anova(m1)
anova(m2)
y <- NULL
a[15, ] ## the same with the m2 model, but not the m1
Many exponential regressions
Many exponential regressions
Description
Many exponential regressions.
Usage
expregs(y, x, di, tol = 1e-09, logged = FALSE)
Arguments
y
A vector with positive data (including zeros).
x
A numerical matrix with the predictor variables.
di
A vector of size equal to that of y with 0s and 1s indicating censoring or not
respectively.
tol
The tolerance value to stop the newton-Raphson iterations. It is set to 1e-09 by
default.
logged
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
Details
We have implemented the newton-Raphson in order to avoid unnecessary calculations.
Value
A matrix with three columns, the test statistic, its associated (logged) p-value and the BIC of each
model.
118
Many F-tests with really huge matrices
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
univglms, score.glms, logistic_only,
poisson_only, regression
Examples
## 200 variables, hence 200 univariate regressions are to be fitted
x <- matrnorm(100, 100)
y <- rexp(100, 4)
system.time( expregs(y, x, di = rep(1, length(y))) )
x <- NULL
Many F-tests with really huge matrices
Many F-tests with really huge matrices
Description
Many F-tests with really huge matrices.
Usage
list.ftests(x, logged = FALSE)
Arguments
x
A list with many big size matrices. Each element of the list contains a matrix. This is the ftests function but with really huge matrices, which cannot be
loaded into R as a single matrix.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
The Welch’s F-test (without assuming equal variances) is performed just like in the "ftests" function.
The difference is that you have a really huge matrix which you cannot load into R. In the "ftests"
function, the argument "ina" denotes the different groups. Here, you "cut" the matrix into smaller
ones, each of which denotes a different group and put them in a list.
Many G-square tests of indepedence
119
Value
A matrix with the test statistic and the p-value of each test.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>.
References
B.L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika,
38(3/4), 330-336.
See Also
ftests, ttests
Examples
x <- matrnorm(300, 500)
ina <- rbinom(300, 2, 0.6) + 1
a <- list()
a[[ 1 ]] <- x[ina == 1, ]
a[[ 2 ]] <- x[ina == 2, ]
a[[ 3 ]] <- x[ina == 3, ]
mod <- list.ftests(a)
z <- NULL
a <- NULL
Many G-square tests of indepedence
Many G-square tests of indepedence
Description
Many G-square tests of indepdence with and without permutations.
Usage
g2tests(data, x, y, dc)
g2tests_perm(data, x, y, dc, nperm)
120
Many G-square tests of indepedence
Arguments
data
A numerical matrix with the data. The minimum must be 0, otherwise the
function can crash or will produce wrong results.
x
An integer number or a vector of integer numbers showing the other variable(s)
to be used for the G2 test of independence.
y
An integer number showing which column of data to be used.
dc
A numerical value equal to the number of variables (or columns of the data matrix) indicating the number of distinct, unique values (or levels) of each variable.
Make sure you give the correct numbers here, otherwise the degrees of freedom
will be wrong.
nperm
The number of permutations. The permutations test is slower than without permutations and should be used with small sample sizes or when the contigency
tables have zeros. When there are few variables, R’s "chisq.test" function is
faster, but as the number of variables increase the time difference with R’s procedure becomes larger and larger.
Details
The function does all the pairwise G2 test of independence and gives the position inside the matrix.
The user must build the associations matrix now, similarly to the correlation matrix. See the examples of how to do that. The p-value is not returned, we leavve this to the user. See the examples of
how to obtain it.
Value
A list including:
statistic
The G2 test statistic for each pair of variables.
pvalue
This is returned when you have selected the permutation based G2 test.
x
The row or variable of the data.
y
The column or variable of the data.
df
The degrees of freedom of each test.
Author(s)
Giorgos Borboudakis. The permutation version used a C++ code by John Burkardt.
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
References
Tsagris M. (2017). Conditional independence test for categorical data using Poisson log-linear
model. Journal of Data Science, 15(2):347-356.
Tsamardinos, I., & Borboudakis, G. (2010). Permutation testing improves Bayesian network learning. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases
(pp. 322-337). Springer Berlin Heidelberg.
121
Many Gini coefficients
See Also
g2Test, g2Test_perm, correls, univglms
Examples
nvalues <- 3
nvars <- 10
nsamples <- 2000
data <- matrix( sample( 0:(nvalues - 1), nvars * nsamples, replace = TRUE ), nsamples, nvars )
dc <- rep(nvalues, nvars)
a <- g2tests(data = data, x = 2:9, y = 1, dc = dc)
pval <- pchisq(a$statistic, a$df, lower.tail = FALSE) ## p-value
b <- g2tests_perm(data = data, x = 2:9, y = 1, dc = dc, nperm = 1000)
a<-b<-data<-NULL
Many Gini coefficients
Many Gini coefficients
Description
Many Gini coefficients.
Usage
ginis(x)
Arguments
x
A matrix with non negative data. The rows are observations and the columns
denote the variables.
Details
We have implemented the fast version of the Gini coefficient. See wikipedia for more details.
Value
A vector with the Gini coefficient, one for each variable.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
122
Many hypothesis tests for two means of percentages
See Also
colskewness, colmeans, corpairs
Examples
x <- matrix( rpois(500 * 1000, 1000), ncol = 1000 )
a <- ginis(x)
Many hypothesis tests for two means of percentages
Many hypothesis tests for two means of percentages
Description
Many hypothesis tests for two means of percentages.
Usage
percent.ttests(x, y, logged = FALSE)
Arguments
x
A numericalmatrix with the percentages of the first sample. Any value between
0 and 1 (inclusive) is allowed.
y
A numerical matrix with the percentages of the first sample. Any value between
0 and 1 (inclusive) is allowed.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
This is the prop.reg but with a single categorical predictor which has two levels only. It is like a
t-test for the means of two samples haivng percentages.
Value
A matrix with three columns, the phi parameter, the test statistic and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Many moment and maximum likelihood estimations of variance components
123
References
Papke L. E. & Wooldridge J. (1996). Econometric methods for fractional response variables with
an application to 401(K) plan participation rates. Journal of Applied Econometrics, 11(6): 619-632.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
link{percent.ttest}, prop.reg, ttest2, ftest
Examples
x <- matrix( rbeta(100 * 10, 3, 1), ncol = 10)
y <- matrix( rbeta(50 * 10, 7.5, 2.5), ncol = 10)
percent.ttests(x, y)
Many moment and maximum likelihood estimations of variance components
Many moment and maximum likelihood estimations of variance components
Description
Many moment and maximum likelihood estimations of variance components.
Usage
colvarcomps.mom(x, id, parallel = FALSE)
colvarcomps.mle(x, id, ranef = FALSE, tol= 1e-08, maxiters = 100,
parallel = FALSE)
Arguments
x
A matrix with the data, where each column refers to a different sample of subjects.
id
A numerical vector indicating the subject. You must put consecutive numbers
and no zero values. Alternatively this can be a factor variable.
ranef
Do you also want the random effects to be returned? TRUE or FALSE.
tol
The tolerance level to terminate the golden ratio search.
maxiters
The maximum number of iterations to perform.
parallel
Should the computations run in parallel? TRUE or FALSE.
124
Many moment and maximum likelihood estimations of variance components
Details
Note that the "colvarcomp.mom" works for balanced designs only, i.e. for each subject the same
number of measurements have been taken. The "colvarcomps.mle" works for unbalanced as well.
The variance components, the variance of the between measurements and the variance of the within
are estimated using moment estimators. The "colvarcomps.mom" is the moment analogue of a
random effects model which uses likelihood estimation ("colvarcomps.mle"). It is much faster, but
can give negative variance of the random effects, in which case it becomes zero.
The maximum likelihood version is a bit slower (try youselves to see the difference), but statistically
speaking is to be preferred when small samples are available. The reason why it is only a little
bit slower and not a lot slower as one would imagine is because we are using a closed formula
to calculate the two variance components (Demidenko, 2013, pg. 67-69). Yes, there are closed
formulas for linear mixed models.
Value
For the "colvarcomps.mom": A matrix with 5 columns, The MSE, the estimate of the between
variance, the variance components ratio and a 95% confidence for the ratio.
For the "colvarcomps.mle": If ranef = FALSE a list with a single component called "info". That
is a matrix with 3 columns, The MSE, the estimate of the between variance and the log-likelihood
value. If ranef = TRUE a list including "info" and an extra component called "ranef" containing the
random effects. It is a matrix with the same number of columns as the data. Each column contains
the randome effects of each variable.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
D.C. Montgomery (2001). Design and analysis of experiments (5th Edition). New York: John
Wiley \& Sons.
Charles S. Davis (2002). Statistical methods for the analysis of repeated measures. New York:
Springer-Verlag.
Demidenko E. (2013). Mixed Models: Thoery and Applications with R 2nd Edition). New Jersey:
John Wiley \& Sons (Excellent book).
See Also
varcomps.mle, colrint.regbx
Examples
## example taken from Montgomery, page 514-517.
y <- c(98, 97, 99, 96, 91, 90, 93, 92,
96, 95, 97, 95, 95, 96, 99, 98)
Many multi-sample tests
125
y <- matrix(y)
id <- rep(1:4, each = 4)
x <- rmvnorm(100, numeric(100), diag(rexp(100)) )
id <- rep(1:25, each = 4)
n <- 25 ; d <- 4
a <- colvarcomps.mom(x, id)
mean(a[, 4]<0 & a[, 5]>0)
b <- colvarcomps.mle(x, id)
x <- NULL
Many multi-sample tests
Many multi-sample tests
Description
Many multi-sample tests.
Usage
ftests(x, ina, logged = FALSE)
anovas(x, ina, logged = FALSE)
vartests(x, ina, type = "levene", logged = FALSE)
block.anovas(x, treat, block, logged = FALSE)
Arguments
x
A matrix with the data, where the rows denote the observations (and the two
groups) and the columns are the variables.
ina
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Be careful, the function is desinged to accept numbers greater than zero. Alternatively
it can be a factor variable.
type
This is for the variances test and can be either "levene" or "bf" corresponding to
Levene’s or Brown-Forsythe’s testing procedure.
treat
In the case of the blocking ANOVA this argument plays the role of the "ina"
argument.
block
This item, in the blocking ANOVA denotes the subjects which are the same.
Similarly to "ina" a numeric vector with 1s, 2s, 3s and so on.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
126
Many multi-sample tests
Details
The Welch’s F-test (without assuming equal variances) is performed with the "ftests" function. The
"anovas" function perform the classical (Fisher’s) one-way analysis of variance (ANOVA) which
assumes equal variance across the groups.
The "vartests" perform hypothesis test for the equality of the variances in two ways, either via
the Levene or via the Brown-Forshythe procedure. Levene’s test employs the means, whereas
the Brown-Forsythe procedure employs the medians and is therefore more robust to outliers. The
"var2tests" implement the classical F test.
The "block.anova" is the ANOVA with blocking, randomised complete block design (RCBD). In
this case, for every combination of the block and treatment values, there is only one observation.
The mathematics are the same as in the case of two way ANOVA, but the assumptions different and
the testing procedure also different. In addition, no interaction is present.
Value
A matrix with the test statistic and the p-value of each test.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
B.L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika,
38(3/4), 330-336.
D.C. Montgomery (2001). Design and analysis of experiments (5th Edition). New York: John
Wiley \& Sons
See Also
ttests
Examples
x <- matrix( rnorm(300 * 50), ncol = 50 )
## 300 observations in total
ina <- rbinom(300, 3, 0.6) + 1
a1 <- ftests(x, ina)
a2 <- anovas(x, ina)
a3 <- vartests(x, ina)
x <- NULL
Many multivariate simple linear regressions coefficients
127
Many multivariate simple linear regressions coefficients
Many multivariate simple linear regressions coefficients
Description
Many multivariate simple linear regressions coefficients.
Usage
mvbetas(y, x, pvalue = FALSE)
Arguments
y
A matrix with the data, where rows denotes the observations and the columns
contain the dependent variables.
x
A numerical vector with one continuous independent variable only.
pvalue
If you want a hypothesis test that each slope (beta coefficient) is equal to zero
set this equal to TRUE. It will also produce all the correlations between y and x.
Details
It is a function somehow opposite to the allbetas. Instead of having one y and many xs we have
many ys and one x.
Value
A matrix with the constant (alpha) and the slope (beta) for each simple linear regression. If the
p-value is set to TRUE, the correlation of each y with the x is calculated along with the relevant
p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
allbetas, correls, univglms
128
Many non parametric multi-sample tests
Examples
y
x
a
b
z
<<<<<-
matrnorm(100, 100)
rnorm(100)
mvbetas(y, x, pvalue = FALSE)
matrix(nrow = 100, ncol = 2)
cbind(1, x)
system.time( a <- mvbetas(y, x) )
system.time( for (i in 1:100) b[i, ] = coef( lm.fit( z, y[, i] ) )
y <- NULL
)
Many non parametric multi-sample tests
Many multi-sample tests
Description
Many multi-sample tests.
Usage
kruskaltests(x, ina, logged = FALSE)
cqtests(x, treat, block, logged = FALSE)
Arguments
x
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables.
ina
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Be
careful, the function is desinged to accept numbers greater than zero.
treat
In the case of the Cochran’s Q test, this argument plays the role of the "ina"
argument.
block
This item denotes the subjects which are the same. Similarly to "ina" a numeric
vector with 1s, 2s, 3s and so on.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
The "kruskaltests" performs the Kruskal-Wallis non parametric alternative to analysis of variance
test. The "cqtests" performs the Cocrhan’s Q test for the equality of more than two groups whose
values are strictly binary (0 or 1). This is a generalisation of the McNemar’s test in the multi-sample
case.
Value
A matrix with the test statistic and the p-value of each test.
129
Many odds ratio tests
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
block.anovas, ftests
Examples
x <- matrix( rexp(300 * 200), ncol = 200 )
ina <- rbinom(300, 3, 0.6) + 1
system.time( kruskaltests(x, ina) )
x <- matrix( rbinom(300 * 200, 1, 0.6), ncol = 200 )
treat <- rep(1:3, each = 100)
block <- rep(1:3, 100)
system.time( cqtests(x, treat, block) )
x <- NULL
Many odds ratio tests Many odds ratio tests
Description
It performs very many odds ratio tests.
Usage
odds(x, y = NULL, ina, logged = FALSE)
Arguments
x
A matrix with the data, where the rows denote the samples and the columns are
the variables. They must be 0s and 1s only.
y
A second matrix with the data of the second group. If this is NULL (default
value) then the argument ina must be supplied. Notice that when you supply the
two matrices the procedure is two times faster. They must be 0s and 1s only.
ina
A numerical vector with 1s and 2s indicating the two groups. Be careful, the
function is designed to accept only these two numbers. In addition, if your "y"
is NULL, you must specify "ina".
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
Many odds ratio tests are performed.
130
Many one sample goodness of fit tests for categorical data
Value
A matrix with the test statistic and the p-value (or their logarithm) of each test.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Mosteller Frederick (1968). Association and Estimation in Contingency Tables. Journal of the
American Statistical Association. 63(321):1-28.
Edwards A.W.F. (1963). The measure of association in a 2x2 table. Journal of the Royal Statistical
Society, Series A. 126(1):109-114.
See Also
odds.ratio, g2Test_univariate
Examples
x <- matrix(rbinom(100 * 500, 1, 0.5), ncol = 500)
ina <- rep(1:2, each = 50)
a <- odds(x,ina=ina)
Many one sample goodness of fit tests for categorical data
Many one sample goodness of fit tests for categorical data
Description
Many one sample goodness of fit tests for categorical data.
Usage
cat.goftests(x, props, type = "gsquare", logged = FALSE)
Arguments
x
props
type
logged
A matrix with the data, where the rows denote the samples and the columns are
the variables. The data must be integers and be of the form 1, 2, 3, and so on.
The minimum must be 1, and not zero.
The assumed distribution of the data. A vector or percentages summing to 1.
Either Pearson’s χ2 test ("chisquare") is used or the G2 test ("qsquare", default
value).
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Many one sample tests
131
Details
Given a matrix of integers, where each column refers to a sample, the values of a categorical variable
the function tests wether these values can be assumed to fit a specific distribution.
Value
A matrix with the test statistic and the p-value of each test.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
ttests, ttest, ftests
Examples
x <- matrix( rbinom(300 * 100, 4, 0.6), ncol = 100 ) + 1
props <- dbinom(0:4, 4, 0.6)
## can we assume that each column comes from a distribution whose mass is given by props?
system.time( cat.goftests(x, props) )
a1 <- cat.goftests(x, props) ## G-square test
a2 <- cat.goftests(x, props, type = "chisq") ## Chi-square test
cor(a1, a2)
mean( abs(a1 - a2) )
x <- NULL
Many one sample tests Many one sample tests
Description
Many one sample tests.
Usage
proptest(x, n, p, alternative = "unequal", logged = FALSE)
ttest(x, m, alternative = "unequal", logged = FALSE, conf = NULL)
vartest(x, sigma, alternative = "unequal", logged = FALSE, conf = NULL)
132
Many one sample tests
Arguments
x
A matrix with numerical data. Each column of the matrix corresponds to a
sample, or a group. In the case of the "proptest" this is a vector integers ranging
from 0 up to n. It is the number of "successes".
n
This is for the "proptest" only and is a vector with integer numbers specifying
the number of tries for the proptest. Its size is equal to the size of x.
p
A vector with the assumed probabilities of success in the "proptest". Its size is
equal to the number of colums of the matrix x.
m
A vector with the assumed means. Its size is equal to the number of colums of
the matrix x.
sigma
A vector with assumed variances. Its size is equal to the number of colums of
the matrix x.
alternative
The type of hypothesis to be checked. Equal to ("unequal"), grater than("greater")
or less than ("less") the assumed parameter.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
conf
If you want confidence intervals to be returned specify the confidence level,
otherwise leave it NULL.
Details
Despite the functions having been written in R, they are very fast.
Value
For all tests except for the "sftests" a matrix with two colums, the test statistic and the p-value
respectively.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
ftests, ttests
Examples
R <- 100
## protest
x <- rbinom(R, 50, 0.6)
n <- rep(50, R)
p <- rep(0.6, R)
a1 <- proptest(x, n, p, "unequal", logged = FALSE)
sum( a1[, 2] < 0.05 ) / R
Many random intercepts LMMs for balanced data with a single identical covariate.
133
## vartest
x <- matrnorm(100, 100)
a2 <- vartest(x, rep(1, R) )
sum( a2[, 2] < 0.05 )
## ttest
a4 <- ttest(x, numeric(R) )
sum(a4[, 2] < 0.05) / R
x <- NULL
Many random intercepts LMMs for balanced data with a single identical covariate.
Many random intercepts LMMs for balanced data with a single identical covariate
Description
Many random intercepts LMMs for balanced data with a single identical covariate.
Usage
colrint.regbx(y, x, id)
Arguments
y
A numerical matrix with the data. The subject values.
x
A numerical vector with the same length as the number of rows of y indicating
the fixed predictor variable. Its values are the same for all levels of y. An
example of this x is time which is the same for all subjects.
id
A numerical variable with 1, 2, ... indicating the subject.
Details
This is a special case of a balanced random intercepts model with a compound symmetric covariance
matrix and one single covariate which is constant for all replicates. An example, is time, which is
the same for all subjects. Maximum likelihood estimation has been performed. In this case the
mathematics exist in a closed formula (Demidenko, 2013, pg. 67-69).
This is the generalistion of rint.regbx to matrices. Assume you have many observations, gene
expressions over time for example, and you want to calculate the random effects or something else
for each expression. Instead of using a "for" loop with rint.regbx function we have used amtrix
operations to make it even faster.
134
Many regression based tests for single sample repeated measures
Value
A list including:
info
A matrix with the random intercepts variance (between), the variance of the
errors (within), the log-likelihood, the deviance (twice the log-likelihood) and
the BIC. In the case of "rint.reg" it also includes the number of iterations required
by the generalised least squares.
be
The estimated regression coefficients, which in the case of "rint.regbx" are simply two: the constant and the slope (time effect).
ranef
A matrix with random intercepts effects. Each row corresponds to a column in
y. Instead of having a matrix with the same number of columns as y we return a
transposed matrix.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Eugene Demidenko (2013). Mixed Models: Theory and Applications with R, 2nd Edition. New
Jersey: Wiley \& Sons (excellent book).
See Also
colvarcomps.mle, rint.regbx, rm.lines, varcomps.mom, rint.reg
Examples
y <- matrix( rnorm(100 * 50), ncol = 50)
id <- rep(1:20, each = 5)
x <- rep(1:10, 10)
system.time( a<- colrint.regbx(y, x, id) )
x <- NULL
Many regression based tests for single sample repeated measures
Many regression based tests for single sample repeated measures
Description
Many regression based tests for single sample repeated measures.
Usage
rm.lines(y, x, logged = FALSE)
rm.anovas(y, x, logged = FALSE)
Many regression based tests for single sample repeated measures
135
Arguments
y
A matrix with the data, where each column refers to a different sample of subjects. For example, the first column is the repeated measurements of a sample of
subjects, the second column contains repeated measurements of a second sample
of subjects and so on. Within each column, the measurements of each subjects
are stacked one upon the other. Say for examples there are n subjects and each
of them has been measured d times (in time or at different experimental conditions). We put these in a matrix with just one column. The first d rows are the
measurements of subject 1, the next d rows are the measurements of subject 2
and so on.
x
A numerical vector with time (usually) or the the predictor variable. For example
the temperature, or the pressure. See the details for more information. Its length
is equal to the time points for example, i.e. it must not have the same length as
the number of rows of y. For the "rm.lines" this is a continuous variable.
For the "rm.anovas" this is treated as a categorical variable, indicating say the
type of experimental condition, but no difference between the points is important. Hence, for this function only, x can also be a facto variable.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
In order to see whether the repeated measurements are associated with a single covariate, e.g. time
we perform many regressions and each time calculate the slope. For each subject, its regression
slope with the covariate is calculated. In the end a t-test for the hypothesis that the average slopes
is zero is performed. The regression slopes ignore that the measurements are not independent, but
note that the slopes are independent, because they come from different subjects. This is a simple,
summary statistics based approach found in Davis (2002), yet it can provide satisfactory results.
The second approach ("rm.anovas") found in Davis (2002) is the usual repeated measures ANOVA.
In this case, suppose you have taken measurements on one or more variables from the same group
of people. See the example below on how to put such data.
Value
A matrix with the test statistic (t-test) and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Charles S. Davis (2002). Statistical methods for the analysis of repeated measures. Springer-Verlag,
New York.
136
Many score based GLM regressions
See Also
rint.regbx, rint.reg, varcomps.mle
Examples
y <- c(74.5,81.5,83.6,68.6,73.1,79.4,
75.5,84.6,70.6,87.3,73.0,75.0,
68.9,71.6,55.9,61.9,60.5,61.8,
57.0,61.3,54.1,59.2,56.6,58.8,
78.3,84.9,64.0,62.2,60.1,78.7,
54.0,62.8,63.0,58.0,56.0,51.5,
72.5,68.3,67.8,71.5,65.0,67.7,
80.8,89.9,83.2,83.0,85.7,79.6)
y <- as.matrix(y)
### the first 6 measurements are from subject 1, measurments 7-12 are from subject 2,
## measurements 13-18 are from subject 3 and so on.
x <- c(-10, 25, 37, 50, 65, 80) ## all subjects were measured at the same time points
rm.lines(y, x) ## Is linear trend between the measurements and the temperature?
rm.anovas(y, x) ## Tests whether the means of the individuals are the same
## the temperature is treated as categorical variable here.
## fake example
y <- matrnorm(10, 4)
## the y matrix contains 4 repeated measurements for each of the 10 persons.
x <- 1:4
## we stack the measurements of each subject, one under the other in a matrix form.
y1 <- matrix( t(y) )
rm.anovas(y1, x) ## perform the test
z <- matrix( rnorm(20 * 8), ncol = 2) ## same example, but with 2 sets of measurements.
rm.anovas(z, x)
Many score based GLM regressions
Many score based GLM regressions
Description
Many score based GLM regressions.
Usage
score.glms(y, x, oiko = NULL, logged = FALSE )
score.multinomregs(y, x, logged = FALSE )
score.negbinregs(y, x, logged = FALSE )
137
Many score based GLM regressions
Arguments
y
A vector with either discrete or binary data for the Poisson or negative binomial
and binary logistic regression respectively. Otherwise it is a vector with discrete
values or factor values for the multinomial regression. If the vector is binary and
choose multinomial regression the function checks and transfers to the binary
logistic regression.
x
A matrix with data, the predictor variables.
oiko
This can be either "poisson" or "binomial". If you are not sure leave it NULL
and the function will check internally.
logged
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
Details
Instead of maximising the log-likelihood via the Newton-Raphson algorithm in order to perform the
hypothesis testing that βi = 0 we use the score test. This is dramatcially faster as no model needs to
be fitted. The first derivative (score) of the log-likelihood is known and in closed form and under the
null hypothesis the fitted values are all equal to the mean of the response variable y. The variance
of the score is also known in closed form. The test is not the same as the likelihood ratio test. It is
size correct nonetheless but it is a bit less efficient and less powerful. For big sample sizes though
(5000 or more) the results are the same. It is also much faster then the classical log-likelihood ratio
test.
Value
A matrix with two columns, the test statistic and its associated p-value. For the Poisson and logistic
regression the p-value is derived via the t distribution, whereas for the multinomial regressions via
the χ2 distribution.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Campbell, M.J. (2001). Statistics at Square Two: Understand Modern Statistical Applications in
Medicine, pg. 112. London, BMJ Books.
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
Agresti Alan (1996). An introduction to categorical data analysis. New York: Wiley.
Joseph M.H. (2011). Negative Binomial Regression. Cambridge University Press, 2nd edition.
See Also
univglms, logistic_only,
poisson_only, regression
138
Many score based regression models
Examples
x <- matrnorm(500, 500)
y <- rbinom(500, 1, 0.6)
## binary logistic regression
a1 <- univglms(y, x)
system.time( score.glms(y, x) )
a2 <- score.glms(y, x)
x <- NULL
cor(a1, a2)
mean(a1 - a2)
Many score based regression models
Many score based regression models.
Description
Many score based regression models.
Usage
score.weibregs(y, x, logged = FALSE)
score.betaregs(y, x, logged = FALSE)
score.gammaregs(y, x, logged = FALSE)
score.expregs(y, x, logged = FALSE)
score.invgaussregs(y, x, logged = FALSE)
score.ztpregs(y, x, logged = FALSE)
score.geomregs(y, x, logged = FALSE)
Arguments
y
A vector with data. For the Weibull, gamma and exponential regressions they
must be strictly positive data, lifetimes or durations for example. For the beta
regression they must be numbers between 0 and 1. For the zero truncated Poisson regression (score.ztpregs) they must be integer valued data strictly greater
than 0.
x
A matrix with data, the predictor variables.
logged
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
Details
Instead of maximising the log-likelihood via the Newton-Raphson algorithm in order to perform
the hypothesis testing that βi = 0 we use the score test. This is dramatcially faster as no model
need to be fitted. The first derivative of the log-likelihood is known in closed form and under the
null hypothesis the fitted values are all equal to the mean of the response variable y. The test is not
the same as the likelihood ratio test. It is size correct nonetheless but it is a bit less efficient and
less powerful. For big sample sizes though (5000 or more) the results are the same. You cna try for
139
Many Shapiro-Francia normality tests
yourselves and see that even with 500 the results are pretty close. The score test is also very faster
then the classical likelihood ratio test.
What we have seen via simulation studies is that it is size correct to large sample sizes, at elast a
few thousands.
Value
A matrix with two columns, the test statistic and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
Campbell, M.J. (2001). Statistics at Square Two: Understand Modern Statistical Applications in
Medicine, pg. 112. London, BMJ Books.
See Also
score.glms univglms, logistic_only,
poisson_only, regression
Examples
x <- matrnorm(300, 100)
y <- rweibull(300, 2, 3)
a <- score.weibregs(y, x)
sum(a[, 2] < 0.05) / 100
x <- NULL
Many Shapiro-Francia normality tests
Many Shapiro-Francia normality tests
Description
Many Shapiro-Francia normality tests.
Usage
sftests(x, logged = FALSE)
sftest(x, logged = FALSE)
140
Many Shapiro-Francia normality tests
Arguments
x
A matrix with the data, where the rows denote the observations and the columns
are the variables. In the case of a single sample, then this must be a vector and
"sftest" is to be used.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
The Shapiro-Francia univariate normality test is performed for each column (variable) of the matrix
x.
Value
A matrix with the squared correlation between the ordered values and the standard normal ordered
statistics, the test statistic and the p-value of each test. If the "sftest" has been used, the output is a
vector with these three elements.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Royston J. P. (1983). A simple method for evaluating the Shapiro-Francia W’ test of non-normality.
The Statistician, 32(3): 297-300.
Mbah A. K. & Paothong A. (2015). Shapiro-Francia test compared to other normality test using
expected p-value. Journal of Statistical Computation and Simulation, 85(15): 3002-3016.
See Also
ttests, ttest, ftests
Examples
x <- matrnorm(200, 100)
system.time( sftests(x) )
a <- sftests(x)
mean(a[, 3]<0.05)
x <- rnorm(100)
sftest(x)
Many simple circular or angular regressions
141
Many simple circular or angular regressions
Many simple circular or angular regressions
Description
Many regressions with one circular dependent variable and one Euclidean independent variable.
Usage
spml.regs(y, x, tol = 1e-07, logged = FALSE, maxiters = 100, parallel = FALSE)
Arguments
y
The dependent variable, it can be a numerical vector with data expressed in
radians or it can be a matrix with two columns, the cosinus and the sinus of
the circular data. The benefit of the matrix is that if the function is to be called
multiple times with the same response, there is no need to transform the vector
every time into a matrix.
x
A matrix with independent variable.
tol
The tolerance value to terminatate the Newton-Raphson algorithm.
logged
Do you want the logarithm of the p-value be returned? TRUE or FALSE.
maxiters
The maximum number of iterations to implement.
parallel
Do you want the calculations to take plac ein parallel? The default value if
FALSE.
Details
The Newton-Raphson algorithm is fitted in these regression as described in Presnell et al. (1998).
For each colum of x a circual regression model is fitted and the hypothesis testing of no association
between y and this variable is performed.
Value
A matrix with two columns, the test statistics and their associated (log) p-values.
Author(s)
Michail Tsagris and Stefanos Fafalios
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Stefanos Fafalios
<stefanosfafalios@gmail.com>
References
Presnell Brett, Morrison Scott P. and Littell Ramon C. (1998). Projected multivariate linear models
for directional data. Journal of the American Statistical Association, 93(443): 1068-1077.
142
Many simple Gaussian regressions with a log-link
See Also
spml.mle, iag.mle, acg.mle
Examples
x
z
y
y
x
a
x
<<<<<<<-
rnorm(100)
cbind(3 + 2 * x, 1 -3 * x)
cbind( rnorm(100,z[ ,1], 1), rnorm(100, z[ ,2], 1) )
y / sqrt( rowsums(y^2) )
matrnorm(100, 100)
spml.regs(y, x)
NULL
Many simple Gaussian regressions with a log-link
Many simple Gaussian regressions with a log-link
Description
Many simple Gaussian regressions with a log-link.
Usage
normlog.regs(y, x, tol = 1e-08, logged = FALSE, parallel = FALSE, maxiters = 100)
Arguments
y
The dependent variable, a numerical variable with non negative numbers.
x
A matrix with the indendent variables.
tol
The tolerance value to terminate the Newton-Raphson algorithm.
logged
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
parallel
Do you want this to be executed in parallel or not. The parallel takes place in
C++, therefore you do not have the option to set the number of cores.
maxiters
The maximum number of iterations that can take place in each regression.
Details
Many simple Gaussian regressions with a log-link are fitted.
Value
A matrix with the test statistic values, their relevant (logged) p-values and the BIC values.
Author(s)
Stefanos Fafalios
R implementation and documentation: Stefanos Fafalios <stefanosfafalios@gmail.com>
Many simple geometric regressions
143
See Also
normlog.reg, score.glms, prop.regs, allbetas
Examples
y <- abs( rnorm(100) )
x <- matrnorm(100, 100)
a <- normlog.regs(y, x)
b <- glm(y ~ x[, 1], family = gaussian(log) )
anova(b, test= "Chisq")
a[1, ]
x <- NULL
Many simple geometric regressions
Many simple geometric regressions.
Description
Many simple geometric regressions.
Usage
geom.regs(y, x, tol = 1e-07, type = 1, logged = FALSE, parallel = FALSE, maxiters = 100)
Arguments
y
The dependent variable, count data.
x
A matrix with the indendent variables.
tol
The tolerance value to terminate the Newton-Raphson algorithm.
type
Type 1 refers to the case where the minimum is zero and type 2 for the case of
the minimum being 1.
logged
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
parallel
Do you want this to be executed in parallel or not. The parallel takes place in
C++, and the number of threads is defined by each system’s availiable cores.
maxiters
The max number of iterations that can take place in each regression.
Details
Many simple geometric regressions are fitted.
Value
A matrix with the test statistic values, their relevant (logged) p-values and the BIC values.
144
Many simple linear mixed model regressions
Author(s)
Stefanos Fafalios
R implementation and documentation: Stefanos Fafalios <stefanosfafalios@gmail.com>
See Also
poisson_only, prop.regs, score.geomregs
Examples
y
x
a
x
<<<<-
rgeom(100, 0.6)
matrix( rnorm(100 * 50), ncol = 50)
geom.regs(y, x)
NULL
Many simple linear mixed model regressions
Many simple linear mixed model regressions
Description
Many simple linear mixed model regressions with random intercepts only.
Usage
rint.regs(y, x, id, tol = 1e-08, logged = FALSE, parallel = FALSE, maxiters = 100)
Arguments
y
A numerical vector with the data. The subject values, the clustered data.
x
A numerical matrix with data ,the independent variables.
id
A numerical variable with 1, 2, ... indicating the subject. Unbalanced design is
of course welcome.
tol
The tolerance value to terminate the Newton-Raphson algorithm. This is set to
10−9 by default.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
parallel
Do you want this to be executed in parallel or not. The parallel takes place in
C++, and the number of threads is defined by each system’s availiable cores.
maxiters
The max number of iterations that can take place in each regression.
Details
Many linear mixed models with a single covariate are fitted. We use Newton-Raphson as described
in Demidenko (2013). The test statistic is the usual F-test. This model allows for random intercepts
only.
Many simple linear regressions coefficients
145
Value
A two-column matrix with the test statistics (Wald statistic) and the associated p-values (or their
loggarithm).
Author(s)
Stefanos Fafalios
R implementation and documentation: Stefanos Fafalios <stefanosfafalios@gmail.com>
References
Eugene Demidenko (2013). Mixed Models: Theory and Applications with R, 2nd Edition. New
Jersey: Wiley \& Sons (excellent book).
See Also
rint.reg, allbetas univglms, score.glms, logistic_only
Examples
## not a so good example
y <- rnorm(100)
id <- sample(1:10, 100, replace = TRUE)
x <- matrix( rnorm(100 * 100), ncol = 100)
a <- rint.regs(y, x, id)
x <- NULL
Many simple linear regressions coefficients
Simple linear regressions coefficients
Description
Simple linear regressions coefficients.
Usage
allbetas(y, x, pvalue = FALSE, logged = FALSE)
Arguments
y
x
pvalue
logged
A numerical vector with the response variable. If the y contains proportions or
percentages, i.e. values between 0 and 1, the logit transformation is applied first
and the transformed data are used.
A matrix with the data, where rows denotes the observations and the columns
contain the independent variables.
If you want a hypothesis test that each slope (beta coefficient) is equal to zero
set this equal to TRUE. It will also produce all the correlations between y and x.
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
146
Many simple multinomial regressions
Value
A matrix with the constant (alpha) and the slope (beta) for each simple linear regression. If the
p-value is set to TRUE, the correlation of each y with the x is calculated along with the relevant test
statistic and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
mvbetas, correls, univglms, colsums, colVars
Examples
x
y
r
a
x
<<<<<-
matrix( rnorm(100 * 50), ncol = 50 )
rnorm(100)
cor(y, x) ## correlation of y with each of the xs
allbetas(y, x) ## the coefficients of each simple linear regression of y with x
NULL
Many simple multinomial regressions
Many simple multinomial regressions.
Description
Many simple multinomial regressions.
Usage
multinom.regs(y, x, tol = 1e-08, logged = FALSE, maxiters = 100)
Arguments
y
The dependent variable, either a numerical variable or a factor variable.
x
A matrix with the indendent variables.
tol
The tolerance value to terminate the Newton-Raphson algorithm.
logged
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
maxiters
The maximum number of iterations that can take place in each regression.
Details
Many simple multinomial regressions are fitted.
Many tests for the dispersion parameter in Poisson distribution
147
Value
A matrix with the test statistic values, their relevant (logged) p-values and the BIC values.
Author(s)
Stefanos Fafalios
R implementation and documentation: Stefanos Fafalios <stefanosfafalios@gmail.com>
See Also
poisson_only, prop.regs, score.geomregs
Examples
y
x
a
x
<<<<-
rbinom(100, 2, 0.5)
matrnorm(100, 100)
multinom.regs(y, x)
NULL
Many tests for the dispersion parameter in Poisson distribution
Many tests for the dispersion parameter in Poisson distribution
Description
Many tests for the dispersion parameter in Poisson distribution.
Usage
colpoisdisp.tests(y, alternative = "either", logged = FALSE)
colpois.tests(y, logged = FALSE)
Arguments
y
alternative
logged
A numerical matrix with count data, 0, 1,...
Do you want to test specifically for either over or underspirsion ("either"), overdispersion ("over") or undersispersion ("under")?
Set to TRUE if you want the logarithm of the p-value.
Value
A matrix with two columns, the test statistic and the (logged) p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
148
Many two-way ANOVAs
References
Yang Zhao, James W. Hardin, and Cheryl L. Addy. (2009). A score test for overdispersion in
Poisson regression based on the generalized Poisson-2 model. Journal of statistical planning and
inference 139(4):1514-1521.
Dimitris Karlis and Evdokia Xekalaki (2000). A Simulation Comparison of Several Procedures for
Testing the Poisson Assumption. Journal of the Royal Statistical Society. Series D (The Statistician), 49(3): 355-382.
Bohning, D., Dietz, E., Schaub, R., Schlattmann, P. and Lindsay, B. (1994) The distribution of the
likelihood ratio for mixtures of densities from the one-parameter exponential family. Annals of the
Institute of Statistical Mathematics, 46(): 373-388.
See Also
poisson.mle, negbin.mle, poisson.anova, poisson.anovas, poisson_only
Examples
y <- matrix(rnbinom(100* 50, 10, 0.6), ncol = 50)
a1 <- colpoisdisp.tests(y, "over")
b1 <- colpois.tests(y)
y <- matrix(rpois(100* 50, 10), ncol = 50)
a2 <- colpoisdisp.tests(y, "either")
b2 <- colpois.tests(y)
y <- NULL
Many two-way ANOVAs
Many two-way ANOVAs
Description
Many two-way ANOVAs.
Usage
twoway.anovas(y, x1, x2, interact = FALSE, logged = FALSE)
Arguments
y
x1
x2
interact
logged
A matrix with the data, where the rows denote the observations (and the two
groups) and the columns are the variables.
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Alternatively it can be a factor variable. This is the one factor.
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Alternatively it can be a factor variable. This is the other factor.
A boolean variable specifying whether you want to test for interaction.
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Many univariate generalised linear models
149
Details
The classical two-way ANOVA design is performed. Note that the design must be balanced. For
every combination of values of the two factors, x1 and x2 the same number of observations must
exist. If that’s not the case, regression models must be used.
Value
A matrix with the test statistic and the p-value of each test.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
D.C. Montgomery (2001). Design and analysis of experiments (5th Edition). New York: John
Wiley \& Sons
See Also
ancovas, ftests, ttests
Examples
y <- as.matrix( rnorm(125) )
x1 <- rep(1:5, 25)
x2 <- rep(1:5, each = 25)
x1 <- factor(x1)
x2 <- factor(x2)
anova( lm(y ~ x1 + x2) )
twoway.anovas(y, x1, x2)
anova( lm(y ~ x1*x2) )
twoway.anovas(y, x1, x2, interact = TRUE)
y <- matrnorm(125, 100)
system.time( a1 <- twoway.anovas(y, x1, x2) )
system.time( a2 <- twoway.anovas(y, x1, x2, interact = TRUE) )
y <- NULL
Many univariate generalised linear models
Many univariate generalised linear regressions
Description
It performs very many univariate generalised linear regressions.
150
Many univariate generalised linear models
Usage
univglms(y, x, oiko = NULL, logged = FALSE)
univglms2(y, x, oiko = NULL, logged = FALSE)
Arguments
y
The dependent variable. It can be a factor or a numerical variable with two
values only (binary logistic regression), a discrete valued vector (count data)
corresponding to a poisson regression or a numerical vector with continuous
values (normal regression).
x
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables. For the "univglms" only continuous variables
are allowed. You are advised to standardise the data before hand to avoid numerical overflow or similar issues. If you see NaN in the outcome, this might
be the case. For the "univglms2" categorical variables are allowed and hence
this accepts data.frames. In this case, the categorical variables must be given as
factor variables, otherwise you might get wrong results.
oiko
This can be either "normal", "poisson", "quasipoisson" or "binomial". If you are
not sure leave it NULL and the function will check internally. However, you
might have discrete data (e.g. years of age) and want to perform many simple
linear regressions. In this case you should specify the family.
logged
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
Details
If you specify no family of distributions the function internally checkes the type of your data and
decides on the type of regression to perform. The function is written in C++ and this is why it is
very fast. It can accept thousands of predictor variables. It is usefull for univariate screening. We
provide no p-value correction (such as fdr or q-values); this is up to the user.
Value
A matrix with the test statistic and the p-value for each predictor variable.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
Many univariate simple binary logistic regressions
151
See Also
logistic_only, poisson_only, allbetas, correls, regression
Examples
x <- matrnorm(100, 100)
y <- rbinom(100, 1, 0.6)
## binary logistic regression
system.time( univglms(y, x) )
a1 <- univglms(y, x)
a2 <- numeric(100)
system.time( for (i in 1:100) a2[i] = glm(y ~ x[, i], binomial)$deviance )
a2 <- glm(y ~ 1, binomial)$null.dev - a2
x <- NULL
Many univariate simple binary logistic regressions
Many univariate simple binary logistic regressions
Description
It performs very many univariate simple binary logistic regressions.
Usage
logistic_only(x, y, tol = 1e-09, b_values = FALSE)
Arguments
x
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables. Currently only continuous variables are allowed.
y
The dependent variable; a numerical vector with two values (0 and 1).
tol
The tolerance value to terminate the Newton-Raphson algorithm.
b_values
Do you want the values of the coefficients returned? If yes, set this to TRUE.
Details
The function is written in C++ and this is why it is very fast. It can accept thousands of predictor
variables. It is usefull for univariate screening. We provide no p-value correction (such as fdr or
q-values); this is up to the user.
Value
A vector with the deviance of each simple binayr logistic regression model for each predictor variable.
152
Many univariate simple linear regressions
Author(s)
Manos Papadakis <papadakm95@gmail.com>
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
allbetas, correls, poisson_only, regression
Examples
## 300 variables, hence 300 univariate regressions are to be fitted
x = matrix( rnorm(100 * 300), ncol = 300 )
## 100 observations in total
y = rbinom(100, 1, 0.6)
## binary logistic regression
system.time( logistic_only(x, y) )
a1 = logistic_only(x, y)
a2 <- numeric(300)
system.time( for (i in 1:300) a2[i] = glm(y ~ x[, i], binomial)$deviance )
a2 = as.vector(a2)
all.equal(a1, a2)
a1<-a2<-y<-x<-NULL
Many univariate simple linear regressions
Many univariate simple linear regressions
Description
It performs very many univariate simple linear regressions with or without categorical variables.
Usage
regression(x, y, logged = FALSE)
Many univariate simple linear regressions
153
Arguments
x
A data.frame or a matrix with the data, where the rows denote the samples (and
the two groups) and the columns are the variables. A data frame is expected if
you have categorical predictor variables. If you only have continuous predictor
variables you should the function allbetas instead as it is faster.
y
The dependent variable; a numerical vector.
logged
Do you want the logarithm of the p-values be returned? The default value is
FALSE.
Details
Some parts of the function will be transferred in C++. It can accept thousands of predictor variables.
It is usefull for univariate screening. We provide no p-value correction (such as fdr or q-values);
this is up to the user.
Value
A matrix with two columns, the test statistic value and its corresponding (logged) p-value.
Author(s)
Manos Papadakis <papadakm95@gmail.com>
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
univglms, allbetas, correls, univglms, mvbetas
Examples
y <- rnorm(150)
a <- regression(iris, y)
a
summary(lm(y ~ iris[, 5]) )
## check the F-test
154
Many univariate simple poisson regressions
Many univariate simple poisson regressions
Many univariate simple poisson regressions
Description
It performs very many univariate simple poisson regressions.
Usage
poisson_only(x, y, tol = 1e-09, b_values = FALSE)
Arguments
x
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables. Currently only continuous variables are allowed.
y
The dependent variable; a numerical vector with many discrete values (count
data).
tol
The tolerance value to terminate the Newton-Raphson algorithm.
b_values
Do you want the values of the coefficients returned? If yes, set this to TRUE.
Details
The function is written in C++ and this is why it is very fast. It can accept thousands of predictor
variables. It is usefull for univariate screening. We provide no p-value correction (such as fdr or
q-values); this is up to the user.
Value
A vector with the deviance of each simple poisson regression model for each predictor variable.
Author(s)
Manos Papadakis <papadakm95@gmail.com>
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
univglms, logistic_only, allbetas, regression
Many univariate simple quasi poisson regressions
155
Examples
## 200 variables, hence 200 univariate regressions are to be fitted
x = matrix( rnorm(100 * 200), ncol = 200 )
y = rpois(100, 10)
system.time( poisson_only(x, y) )
b1 = poisson_only(x, y)
b2 = numeric(500)
system.time( for (i in 1:200) b2[i] = glm(y ~ x[, i], poisson)$deviance )
all.equal(b1, b2)
b1<-b2<-x<-y<-NULL
Many univariate simple quasi poisson regressions
Many univariate simple poisson regressions
Description
It performs very many univariate simple poisson regressions.
Usage
quasi.poisson_only(x, y, tol = 1e-09, maxiters = 100)
Arguments
x
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables. Currently only continuous variables are allowed.
y
The dependent variable; a numerical vector with many discrete values (count
data).
maxiters
The maximum number of iterations after which the Newton-Raphson algorithm
is terminated.
tol
The tolerance value to terminate the Newton-Raphson algorithm.
Details
The function is written in C++ and this is why it is very fast. It can accept thousands of predictor
variables. It is usefull for univariate screening. We provide no p-value correction (such as fdr or
q-values); this is up to the user.
156
Many Welch’s F-tests
Value
A matrix with the deviance and the estimated phi parameter (dispersion parameter) of each simple
poisson regression model for each predictor variable.
Author(s)
Manos Papadakis <papadakm95@gmail.com> and Stefanos Fafalios <stefanosfafalios@gmail.com>
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>, Manos Papadakis
<papadakm95@gmail.com> and Stefanos Fafalios <stefanosfafalios@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
poisson_only univglms, logistic_only, allbetas, regression
Examples
## 200 variables, hence 200 univariate regressions are to be fitted
x <- matrix( rnorm(100 * 200), ncol = 200 )
y <- rpois(100, 10)
system.time( poisson_only(x, y) )
b1 <- poisson_only(x, y)
b2 <- quasi.poisson_only(x, y)
b1<-b2<-x<-y<-NULL
Many Welch’s F-tests
Many Welch’s F-tests
Description
Many Welch’s F-tests.
Usage
colanovas(y, x, logged = FALSE)
Arguments
y
x
logged
A numerical vector with the dependent variable.
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables. This must be a matrix with the categorical
variables as numbers, starting from 1. Welch’s F-test is performed for each
variable.
A boolean variable; it will return the logarithm of the pvalue if set to TRUE.
157
Match
Details
For each categorical variable in the x matrix Welch’s F test is performed. This is the opposie of
ftests,where there are many dependent variables and one categorical variable.
Value
A matrix with the test statistic and the p-value for each predictor variable.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Draper, N.R. and Smith H. (1988). Applied regression analysis. New York, Wiley, 3rd edition.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
regression, ftests, allbetas, correls
Examples
y
x
a
x
<- rnorm(100)
<- matrix( rbinom(100 * 50, 2, 0.5) + 1 , ncol = 50)
<- colanovas(y, x)
<- NULL
Match
Match
Description
Return the positions of its first argument that matches in its second.
Usage
Match(x,key=NULL)
Arguments
x
A numeric vector.
key
The value/vector for searching in vector x. For now let it NULL. dont’t use it!.
158
Matrix with all pairs of t-tests
Details
This function implements the R’s \"match\" function. This version basicaly calculates the match(x,sort(unique(x)))
for now. Do not use the argument key!
Value
Returns the position/positions of the given key/keys in the x vector.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
See Also
match
Examples
y <- rnorm(100)
a <- Match(y)
b <-50
all.equal(as.vector(a),as.vector(b))
Matrix with all pairs of t-tests
Matrix with all pairs of t-tests
Description
Matrix with all pairs of t-tests.
Usage
allttests(x, y = NULL, ina, logged = FALSE)
ttests.pairs(x, logged = FALSE)
Arguments
x
A numerical matrix with the data.
y
For the case of "all.tests", if you have the second group or sample provide it
here, otherwise leave it NULL. For the case of "ttests.pairs" this is not required.
ina
If you have the data in one matric then provide this indicator variable separating
the samples. This numerical vector must contain 1s and 2s only as values. For
the case of "ttests.pairs" this is not required.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Matrix with G-square tests of indepedence
159
Details
The function does all the pairwise t-tests assuming unequal variances (Welch’s t-test). The "all.ttests"
does all the pairs formed by "cutting" the matrices x and y in two and everything between them.
The "ttests.pairs" accepts a matrix x and does all the pairs of t-tests. This is similar to the correlation
matrix style.
Value
A list including:
stat
A matrix with t-test statistic for each pair of variables.
pvalue
A matrix with the corresponding p-values.
dof
A matrix with the relevant degrees of freedom.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
ttests, ftests, ttest, g2Test_univariate
Examples
x <- as.matrix( iris[1:100, 1:4] )
ina <- as.numeric(iris[1:100, 5])
a <- allttests(x, ina = ina)
b <- ttests.pairs(x) ## less tests
Matrix with G-square tests of indepedence
Matrix with G-square tests of indepdence
Description
Matrix with G-square tests of indepdence with and without permutations.
Usage
g2Test_univariate(data, dc)
g2Test_univariate_perm(data, dc, nperm)
160
Matrix with G-square tests of indepedence
Arguments
data
A numerical matrix with the data. The minimum must be 0, otherwise the
function can crash or will produce wrong results.
dc
A numerical value equal to the number of variables (or columns of the data matrix) indicating the number of distinct, unique values (or levels) of each variable.
Make sure you give the correct numbers here, otherwise the degrees of freedom
will be wrong.
nperm
The number of permutations. The permutations test is slower than without permutations and should be used with small sample sizes or when the contigency
tables have zeros. When there are few variables, R’s "chisq.test" function is
faster, but as the number of variables increase the time difference with R’s procedure becomes larger and larger.
Details
The function does all the pairwise G2 test of independence and gives the position inside the matrix.
The user must build the associations matrix now, similarly to the correlation matrix. See the examples of how to do that. The p-value is not returned, we live this to the user. See the examples of how
to obtain it.
Value
A list including:
statistic
The G2 test statistic for each pair of variables.
pvalue
This is returned when you have selected the permutation based G2 test.
x
The row or variable of the data.
y
The column or variable of the data.
df
The degrees of freedom of each test.
Author(s)
Giorgos Borboudakis. The permutation version used a C++ code by John Burkardt.
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
References
Tsagris M. (2017). Conditional independence test for categorical data using Poisson log-linear
model. Journal of Data Science, 15(2):347-356.
Tsamardinos, I., & Borboudakis, G. (2010). Permutation testing improves Bayesian network learning. In Joint European Conference on Machine Learning and Knowledge Discovery in Databases
(pp. 322-337). Springer Berlin Heidelberg
See Also
g2Test, g2Test_perm, correls, univglms
Mean - Median absolute deviation of a vector
161
Examples
nvalues <- 3
nvars <- 10
nsamples <- 2000
data <- matrix( sample( 0:(nvalues - 1), nvars * nsamples, replace = TRUE ), nsamples, nvars )
dc <- rep(nvalues, nvars)
system.time( g2Test_univariate(data = data, dc = dc) )
a <- g2Test_univariate(data = data, dc = dc)
pval <- pchisq(a$statistic, a$df, lower.tail = FALSE)
g <- matrix(0, nvars, nvars)
g[ cbind(a$x, a$y) ] <- a$statistic
g <- g + t(g)
diag(g) <- 0
## g ## matrix of G^2 test statistics
g<-a<-dc<-data<-NULL
Mean - Median absolute deviation of a vector
Mean - Median absolute deviation of a vector
Description
Mean - Median absolute deviation of a vector.
Usage
mad2(x,method = "median",na.rm=FALSE)
Arguments
x
A numerical vector.
method
A character vector with values "median", for median absolute deviation or "mean",
for mean absolute deviation.
na.rm
A logical value TRUE/FALSE to remove NAs.
Value
The mean absolute deviation.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
162
Median of a vector
See Also
colMads, med, colMedians
Examples
x <- Rnorm(1000)
mad2(x)
mad(x)
Median of a vector
Median of a vector
Description
Median of a vector.
Usage
med(x,na.rm=FALSE)
Arguments
x
A numerical vector.
na.rm
TRUE or FAlSE for remove NAs if exists.
Details
The function is written in C++ and this is why it is very fast.
Value
The median of the vector of a numbers.
Author(s)
Manos Papadakis <papadakm95@gmail.com>
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
nth, colMedians
Examples
x <- rnorm(1000)
system.time( for (i in 1:100) med(x) )
system.time( for (i in 1:100) median(x) )
Minima and maxima of two vectors/matrices
163
Minima and maxima of two vectors/matrices
Minima and maxima of two vectors/matrices
Description
Minima and maxima of two vectors/matrices.
Usage
Pmax(x, y,na.rm = FALSE)
Pmin(x, y,na.rm = FALSE)
Pmin_Pmax(x, y,na.rm = FALSE)
Arguments
x
y
na.rm
A numerical vector with numbers.
A numerical vector with numbers.
TRUE or FAlSE for remove NAs if exists.
Details
The parallel minima or maxima are returned. This are the same as the base functions pmax and
pmin.
Value
A numerical vector/matrix with numbers, whose length is equal to the length of the initial vectors/matrices containing the maximum or minimum between each pair.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
sort_mat, Sort, colMins
Examples
x <- rnorm(10)
y <- rnorm(10)
Pmax(x, y)
a<-pmax(x, y)
Pmin(x, y)
b<-pmin(x, y)
Pmin_Pmax(x,y) == c(a,b)
a<-b<-x<-y<-NULL
164
minimum and maximum
minimum and maximum
Minimum and maximum of a vector
Description
Minimum and maximum of a vector.
Usage
min_max(x,index=FALSE, percent = FALSE)
Arguments
x
A numerical vector with data. NAs are handled naturally.
index
A boolean value for the indices of the minimum and the maximum value.
percent
A boolean value for the percent of the positive and negative numbers.
Value
A vector with the relevant values, min and max.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, rowMaxs, nth, colrange, colMedians,sort_mat
Examples
x <- rnorm(100 * 500)
s1 <- min_max(x)
s2 <- c(min(x), max(x))
minimum and maximum frequencies
165
minimum and maximum frequencies
Minimum and maximum frequencies of a vector
Description
Minimum and maximum frequencies of a vector.
Usage
freq.min(x,na.rm = FALSE)
freq.max(x,na.rm = FALSE)
Arguments
x
A numerical/integer vector with data but without NAs.
na.rm
TRUE or FAlSE for remove NAs if exists.
Details
Those functions are the same with max(table(x) or min(table(x)) but with one exception. freq.min
and freq.max will return also which value has the minimum/maximum frequency. More Efficient
than max(table(x) or min(table(x)).
Value
A vector with 2 values, the value with minimum/maximum frequency and the frequency.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com> and Marios
Dimitriadis <kmdimitriadis@gmail.com>.
See Also
rowMins, rowMaxs, nth, colrange, colMedians,sort_mat
Examples
x <- rnorm(100)
f1 <- freq.min(x)
f2 <- freq.max(x)
# f1r <- min(table(x))
# f2r <- max(table(x))
# f1[2]==f1r ## the frequencies are the same
# f2[2]==f2r ## the frequencies are the same
166
MLE for multivariate discrete data
MLE for multivariate discrete data
MLE for multivariate discrete data
Description
MLE for multivariate discrete data.
Usage
multinom.mle(x)
dirimultinom.mle(x, tol = 1e-07)
colpoisson.mle(x)
colgeom.mle(x, type = 1)
Arguments
x
A matrix with discrete valued non negative data.
tol
the tolerance level to terminate the Newton-Raphson algorithm for the Dirichlet
multinomial distribution.
type
This is for the geometric distribution only. Type 1 refers to the case where the
minimum is zero and type 2 for the case of the minimum being 1.
Details
For the Poisson and geometric distributions we simply fit independent Poisson and geometric distributions respectively.
Value
A list including:
loglik
A vector with the value of the maximised log-likelihood.
param
A vector of the parameters.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Johnson Norman L., Kotz Samuel and Balakrishnan (1997). Discrete Multivariate Distributions.
Wiley
Minka Thomas (2012). Estimating a Dirichlet distribution. Technical report.
MLE of (hyper-)spherical distributions
167
See Also
poisson.mle, zip.mle, ztp.mle, negbin.mle, poisson.nb
Examples
x <- t( rmultinom(1000, 20, c(0.4, 0.5, 0.1) ) )
multinom.mle(x)
colpoisson.mle(x)
x <- NULL
MLE of (hyper-)spherical distributions
MLE of (hyper-)spherical distributions
Description
MLE of (hyper-)spherical distributions.
Usage
vmf.mle(x, tol = 1e-07)
multivmf.mle(x, ina, tol = 1e-07, ell = FALSE)
acg.mle(x, tol = 1e-07)
iag.mle(x, tol = 1e-07)
Arguments
x
A matrix with directional data, i.e. unit vectors.
ina
A numerical vector with discrete numbers starting from 1, i.e. 1, 2, 3, 4,... or
a factor variable. Each number denotes a sample or group. If you supply a
continuous valued vector the function will obviously provide wrong results.
ell
This is for the multivmf.mle only. Do you want the log-likelihood returned? The
default value is TRUE.
tol
The tolerance value at which to terminate the iterations.
Details
For the von Mises-Fisher, the normalised mean is the mean direction. For the concentration parameter, a Newton-Raphson is implemented. For the angular central Gaussian distribution there
is a constraint on the estimated covariance matrix; its trace is equal to the number of variables.
An iterative algorithm takes place and convergence is guaranteed. Newton-Raphson for the projected normal distribution, on the sphere, is implemented as well. Finally, the von Mises-Fisher
distribution for groups of data is also implemented.
168
MLE of (hyper-)spherical distributions
Value
For the von Mises-Fisher a list including:
loglik
The maximum log-likelihood value.
mu
The mean direction.
kappa
The concentration parameter.
For the multi von Mises-Fisher a list including:
loglik
A vector with the maximum log-likelihood values if ell is set to TRUE. Otherwise NULL is returned.
mi
A matrix with the group mean directions.
ki
A vector with the group concentration parameters.
For the angular central Gaussian a list including:
iter
The number if iterations required by the algorithm to converge to the solution.
cova
The estimated covariance matrix.
For the spherical projected normal a list including:
iters
The number of iteration required by the Newton-Raphson.
mesi
A matrix with two rows. The first row is the mean direction and the second is
the mean vector. The first comes from the second by normalising to have unit
length.
param
A vector with the elements, the norm of mean vector, the log-likelihood and the
log-likelihood of the spherical uniform distribution. The third value helps in
case you want to do a log-likleihood ratio test for uniformity.
Author(s)
Michail Tsagris R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.
Sra, S. (2012). A short note on parameter approximation for von Mises-Fisher distributions: and a
fast implementation of Is(x). Computational Statistics, 27(1): 177–190.
Tyler D. E. (1987). Statistical analysis for the angular central Gaussian distribution on the sphere.
Biometrika 74(3): 579-589.
Paine P.J., Preston S.P., Tsagris M and Wood A.T.A. (2017). An Elliptically Symmetric Angular
Gaussian Distribution. Statistics and Computing (To appear).
See Also
racg, vm.mle, rvmf
MLE of continuous univariate distributions defined on the positive line
169
Examples
m <- c(0, 0, 0, 0)
s <- cov(iris[, 1:4])
x <- racg(100, s)
mod <- acg.mle(x)
mod
cov2cor(mod$cova) ## estimated covariance matrix turned into a correlation matrix
cov2cor(s) ## true covariance matrix turned into a correlation matrix
vmf.mle(x)
x <- rbind( rvmf(100,rnorm(4), 10), rvmf(100,rnorm(4), 20) )
a <- multivmf.mle(x, rep(1:2, each = 100) )
MLE of continuous univariate distributions defined on the positive line
MLE of continuous univariate distributions defined on the positive line
Description
MLE of continuous univariate distributions defined on the positive line.
Usage
gammamle(x, tol = 1e-09)
chisq.mle(x, tol = 1e-09)
weibull.mle(x, tol = 1e-09, maxiters = 100)
lomax.mle(x, tol = 1e-09)
foldnorm.mle(x, tol = 1e-09)
betaprime.mle(x, tol = 1e-09)
logcauchy.mle(x, tol = 1e-09)
loglogistic.mle(x, tol = 1e-09)
halfnorm.mle(x)
invgauss.mle(x)
lognorm.mle(x)
pareto.mle(x)
expmle(x)
exp2.mle(x)
maxboltz.mle(x)
rayleigh.mle(x)
normlog.mle(x)
lindley.mle(x)
Arguments
x
A vector with positive valued data (zeros are not allowed).
tol
The tolerance level up to which the maximisation stops; set to 1e-09 by default.
maxiters
The maximum number of iterations the Newton-Raphson will perform.
170
MLE of continuous univariate distributions defined on the positive line
Details
Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson
algorithm which is faster. See wikipedia for the equations to be solved. For the t distribution we
need the degrees of freedom and estimate the location and scatter parameters. If you want to to fit
an inverse gamma distribution simply do "gamma.mle(1/x)". The log-likelihood and the parameters
are for the inverse gamma.
The "normlog.mle" is simply the normal distribution where all values are positive. Note, this is not
log-normal. It is the normal with a log link. Similarly to the inverse gaussian distribution where the
mean is an exponentiated. This comes from the GLM theory.
Value
Usually a list with three elements, but this is not for all cases.
iters
The number of iterations required for the Newton-Raphson to converge.
loglik
The value of the maximised log-likelihood.
param
The vector of the parameters.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Kalimuthu Krishnamoorthy, Meesook Lee and Wang Xiao (2015). Likelihood ratio tests for comparing several gamma distributions. Environmetrics, 26(8):571-583.
N.L. Johnson, S. Kotz \& N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1
(2nd Edition).
N.L. Johnson, S. Kotz \& N. Balakrishnan (1970). Distributions in statistics: continuous univariate
distributions, Volume 2
Tsagris M., Beneki C. and Hassani H. (2014). On the folded normal distribution. Mathematics,
2(1):12-28.
Sharma V. K., Singh S. K., Singh U. \& Agiwal V. (2015). The inverse Lindley distribution: a
stress-strength reliability model with application to head and neck cancer data. Journal of Industrial
and Production Engineering, 32(3): 162-173.
You can also check the relevant wikipedia pages for these distributions.
See Also
zip.mle, normal.mle, beta.mle
MLE of continuous univariate distributions defined on the real line
171
Examples
x <- rgamma(100, 3, 4)
system.time( for (i in 1:20) gammamle(x) )
## system.time( for (i in 1:20) fitdistr(x,"gamma") )
a <- glm(x ~ 1, gaussian(log) )
normlog.mle(x)
MLE of continuous univariate distributions defined on the real line
MLE of continuous univariate distributions defined on the real line
Description
MLE of continuous univariate distributions defined on the real line.
Usage
normal.mle(x)
gumbel.mle(x, tol = 1e-09)
cauchy.mle(x, tol = 1e-09)
logistic.mle(x, tol = 1e-07)
ct.mle(x, tol = 1e-09)
tmle(x, v = 5, tol = 1e-08)
wigner.mle(x, tol = 1e-09)
laplace.mle(x)
Arguments
x
A numerical vector with data.
v
The degrees of freedom of the t distribution.
tol
The tolerance level up to which the maximisation stops set to 1e-09 by default.
Details
Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson
algorithm which is faster. See wikipedia for the equation to be solved. For the t distribution we need
the degrees of freedom and estimate the location and scatter parameters.
The Cauchy is the t distribution with 1 degree of freedom. If you want to fit such a distribution used
the cauchy.mle and not the t.mle with 1 degree of freedom as it’s faster. The Laplace distribution is
also called double exponential distribution.
The wigner.mle refers to the wigner semicircle distribution.
172
MLE of count data (univariate discrete distributions)
Value
Usually a list with three elements, but this is not for all cases.
iters
The number of iterations required for the Newton-Raphson to converge.
loglik
The value of the maximised log-likelihood.
param
The vector of the parameters.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Johnson, Norman L. Kemp, Adrianne W. Kotz, Samuel (2005). Univariate Discrete Distributions
(third edition). Hoboken, NJ: Wiley-Interscience.
https://en.wikipedia.org/wiki/Wigner_semicircle_distribution
See Also
zip.mle, gammamle, vm.mle
Examples
x <- rt(1000,10)
a <- ct.mle(x)
tmle(x, v = a$nu)
cauchy.mle(x)
normal.mle(x)
logistic.mle(x)
gumbel.mle(x)
MLE of count data (univariate discrete distributions)
MLE of count data
Description
MLE of count data.
MLE of count data (univariate discrete distributions)
173
Usage
zip.mle(x, tol = 1e-09)
ztp.mle(x, tol = 1e-09)
negbin.mle(x, type = 1, tol = 1e-09)
binom.mle(x, N = NULL, tol = 1e-07)
borel.mle(x)
geom.mle(x, type = 1)
logseries.mle(x, tol = 1e-09)
poisson.mle(x)
Arguments
x
A vector with discrete valued data.
type
This argument is for the negative binomial and the geometric distribution. In the
negative binomial you can choose which way your prefer. Type 1 is for smal
sample sizes, whereas type 2 is for larger ones as is faster. For the geometric it
is related to its two forms. Type 1 refers to the case where the minimum is zero
and type 2 for the case of the minimum being 1.
N
This is for the binomial distribution only, specifying the total number of successes. If NULL, it is sestimated by the data.
tol
The tolerance level up to which the maximisation stops set to 1e-09 by default.
Details
Instead of maximising the log-likelihood via a numerical optimiser we used a Newton-Raphson
algorithm which is faster.
See wikipedia for the equation to be solved in the case of the zero inflated distribution. https://en.wikipedia.org/wiki/Zeroinflated_model. In order to avoid negative values we have used link functions, log for the lambda
and logit for the π as suggested by Lambert (1992). As for the zero truncated Poisson see https://en.wikipedia.org/wiki/Zerotruncated_Poisson_distribution.
zip.mle is for the zero inflated Poisson, whereas ztp.mle is for the zero truncated Poisson distribution.
Value
A list including:
mess
This is for the negbin.mle only. If there is no reason to use the negative binomial
distribution a message will appear, otherwise this is NULL.
iters
The number of iterations required for the Newton-Raphson to converge.
loglik
The value of the maximised log-likelihood.
prob
The probability parameter of the distribution. In some distributions this argument might have a different name. For example, param in the zero inflated
Poisson.
174
MLE of distributions defined in the (0, 1) interval
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Lambert Diane (1992). Zero-Inflated Poisson Regression, with an Application to Defects in Manufacturing. Technometrics. 34 (1): 1-14
Johnson Norman L., Kotz Samuel and Kemp Adrienne W. (1992). Univariate Discrete Distributions
(2nd ed.). Wiley
See Also
poisson_only, colrange
Examples
x <- rpois(100, 2)
zip.mle(x)
poisson.mle(x)
## small difference in the two log-likelihoods as expected.
x <- rpois(100, 10)
x[x == 0 ] <- 1
ztp.mle(x)
poisson.mle(x)
## significant difference in the two log-likelihoods.
x <- rnbinom(100, 10, 0.6)
poisson.mle(x)
negbin.mle(x)
MLE of distributions defined in the (0, 1) interval
MLE of distributions defined in the (0, 1) interval
Description
MLE of distributions defined in the (0, 1) interval.
Usage
beta.mle(x, tol = 1e-09)
ibeta.mle(x, tol = 1e-09)
logitnorm.mle(x)
hsecant01.mle(x, tol = 1e-09)
MLE of distributions defined in the (0, 1) interval
175
Arguments
x
tol
A numerical vector with proportions, i.e. numbers in (0, 1) (zeros and ones are
not allowed).
The tolerance level up to which the maximisation stops.
Details
Maximum likelihood estimation of the parameters of the beta distribution is performed via NewtonRaphson. The distributions and hence the functions does not accept zeros. "logitnorm.mle" fits
the logistic normal, hence no nwewton-Raphson is required and the "hypersecant01.mle" uses the
golden ratio search as is it faster than the Newton-Raphson (less calculations)
Value
A list including:
iters
loglik
param
The number of iterations required by the Newton-Raphson.
The value of the log-likelihood.
The estimated parameters. In the case of "hypersecant01.mle" this is called
"theta" as there is only one parameter.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
See Also
diri.nr2,
Examples
x <- rbeta(1000, 1, 4)
system.time( for(i in 1:1000) beta.mle(x) )
beta.mle(x)
ibeta.mle(x)
x <- runif(1000)
hsecant01.mle(x)
logitnorm.mle(x)
ibeta.mle(x)
x <- rbeta(1000, 2, 5)
x[sample(1:1000, 50)] <- 0
ibeta.mle(x)
176
MLE of some circular distributions
MLE of some circular distributions
MLE of some circular distributions
Description
MLE of some circular distributions.
Usage
vm.mle(x, tol = 1e-09)
spml.mle(x, tol = 1e-09, maxiters = 100)
wrapcauchy.mle(x, tol = 1e-09)
Arguments
x
tol
maxiters
A numerical vector with the circular data. They must be expressed in radians.
For the "spml.mle" this can also be a matrix with two columns, the cosinus and
the sinus of the circular data.
The tolerance level to stop the iterative process of finding the MLEs.
The maximum number of iterations to implement.
Details
The parameters of the von Mises, the bivariate angular Gaussian and wrapped Cauchy distributions
are estimated. For the Wrapped Cauchy, the iterative procedure described by Kent and Tyler (1988)
is used. As for the von Mises distribution, we use a Newton-Raphson to estimate the concentration
parameter. The angular Gaussian is described, in the regression setting in Presnell et al. (1998).
Value
A list including:
iters
loglik
param
gamma
mu
The iterations required until convergence. This is returned in the wrapped Cauchy
distribution only.
The value of the maximised log-likelihood.
A vector consisting of the estimates of the two parameters, the mean direction
for both distributions and the concentration parameter kappa and the rho for the
von Mises and wrapped Cauchy respectively.
The norm of the mean vector of the angualr Gaussian distribution.
The mean vector of the angular Gaussian distribution.
Author(s)
Michail Tsagris and Stefanos Fafalios
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Stefanos Fafalios
<stefanosfafalios@gmail.com>
MLE of the inverted Dirichlet distribution
177
References
Mardia K. V. and Jupp P. E. (2000). Directional statistics. Chicester: John Wiley \& Sons.
Sra S. (2012). A short note on parameter approximation for von Mises-Fisher distributions: and a
fast implementation of Is(x). Computational Statistics, 27(1): 177-190.
Presnell Brett, Morrison Scott P. and Littell Ramon C. (1998). Projected multivariate linear models
for directional data. Journal of the American Statistical Association, 93(443): 1068-1077.
Kent J. and Tyler D. (1988). Maximum likelihood estimation for the wrapped Cauchy distribution.
Journal of Applied Statistics, 15(2): 247–254.
See Also
vmf.mle, rvonmises, rvmf
Examples
y <- rcauchy(100, 3, 1)
x <- y
vm.mle(x)
spml.mle(x)
wrapcauchy.mle(x)
x <- NULL
MLE of the inverted Dirichlet distribution
MLE of the inverted Dirichlet distribution
Description
MLE of the inverted Dirichlet distribution.
Usage
invdir.mle(x, tol = 1e-09)
Arguments
x
A matrix with strictly positive data (no zeros are allowed).
tol
The tolerance level up to which the maximisation stops.
Details
Maximum likelihood estimation of the parameters of the inverted is performed via Newton-Raphson.
We took the initial values suggested by Bdiri T. and Bouguila N. (2012) and modified them a bit.
178
MLE of the multivariate normal distribution
Value
A list including:
iters
The number of iterations required by the Newton Raphson.
loglik
The value of the log-likelihood.
param
The estimated parameters.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
References
Bdiri T. and Bouguila N. (2012). Positive vectors clustering using inverted Dirichlet finite mixture
models. Expert Systems with Applications, 39(2): 1869-1882.
See Also
diri.nr2, multinom.mle
Examples
x <- as.matrix(iris[, 1:4])
system.time( for(i in 1:100) invdir.mle(x) )
invdir.mle(x)
MLE of the multivariate normal distribution
MLE of the multivariate normal distribution
Description
MLE of the multivariate normal distribution.
Usage
mvnorm.mle(x)
Arguments
x
A matrix with numerical data.
Details
The mean vector, covariance matrix and the value of the log-likelihood is calculated.
MLE of the ordinal model without covariates
179
Value
A list including:
iters
The number of iterations required for the Newton-Raphson to converge.
loglik
The value of the maximised log-likelihood.
param
The vector of the parameters for the zero inflated Poisson.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Johnson Norman L., Kotz Samuel and Balakrishnan (1997). Discrete Multivariate Distributions.
Wiley
See Also
multinom.mle, dmvnorm, gaussian.nb
Examples
x <- matrnorm(100, 4)
mvnorm.mle(x)
x <- NULL
MLE of the ordinal model without covariates
Natural logarithm of the beta functionMLE of the ordinal model without covariates
Description
MLE of the ordinal model without covariates.
Usage
ordinal.mle(y, link = "logit")
Arguments
y
A numerical vector with values 1, 2, 3,..., not zeros, or an ordered factor.
link
This can either be "logit" or "probit". It is the link function to be used.
180
MLE of the tobit model
Details
Maximum likelihood of the ordinal model (proportional odds) is implemented. See for example the
"polr" command in R or the examples.
Value
A list including:
loglik
The log-likelihood of the model.
a
The intercepts (threshold coefficients) of the model.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
References
Agresti, A. (2002) Categorical Data. Second edition. Wiley.
See Also
beta.mle, diri.nr2
Examples
y <- factor( rbinom(100,3,0.5), ordered = TRUE )
ordinal.mle(y)
ordinal.mle(y, link = "probit")
MLE of the tobit model
MLE of the tobit model
Description
MLE of the tobit model.
Usage
tobit.mle(y, tol = 1e-09)
Arguments
y
A vector with positive valued data and zero values. If there are no zero values, a
simple normal model is fitted in the end.
tol
The tolerance level up to which the maximisation stops; set to 1e-09 by default.
Moment and maximum likelihood estimation of variance components
181
Details
The tobin model is useful for (univariate) positive data with left censoring at zero. There is the
assumption of a latent variable. Tthe values of that variable which are positive concide with the
observed values. If some values are negative, they are left censored and the observed values are
zero. Instead of maximising the log-likelihood via a numerical optimiser we have used a NewtonRaphson algorithm which is faster.
Value
A list with three elements including
iters
The number of iterations required for the Newton-Raphson to converge.
loglik
The value of the maximised log-likelihood.
param
The vector of the parameters.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Tobin James (1958). Estimation of relationships for limited dependent variables. Econometrica.
26(1):24–36.
https://en.wikipedia.org/wiki/Tobit_model
See Also
gammamle, normal.mle
Examples
x <- rnorm(300, 3, 5)
x[ x < 0 ] <- 0
## left censoring. Values below zero become zero
system.time( for (i in 1:100) tobit.mle(x) )
Moment and maximum likelihood estimation of variance components
Moment and maximum likelihood estimation of variance components
Description
Moment and maximum likelihood estimation of variance components.
182
Moment and maximum likelihood estimation of variance components
Usage
rint.mle(x, ina, ranef = FALSE, tol = 1e-09, maxiters = 100)
varcomps.mom(x, ina)
varcomps.mle(x, ina, tol = 1e-09)
Arguments
x
A numerical vector with the data.
ranef
Should the random effects be returned as well? The default value is FALSE.
ina
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Be careful, the function is desinged to accept numbers greater than zero. Alternatively
it can be a factor variable.
tol
The tolerance level to terminate the golden ratio search. the default value is
10^(-9).
maxiters
The maximum number of iterations Newton-Raphson will implement.
Details
Note that the "varcomps.mle" and "varcomp.mom" work for balanced designs only, i.e. for each
subject the same number of measurements have been taken. The "rint.mle" works for both the
balanced and unbalanced designs.
The variance components, the variance of the between measurements and the variance of the within
are estimated using moment estimators. The "colvarcomsp.mom" is the moment analogue of a
random effects model which uses likelihood estimation ("colvarcomps.mle"). It is much faster, but
can give negative variance of the random effects, in which case it becomes zero.
The maximum likelihood version is a bit slower (try youselves to see the difference), but statistically
speaking is to be preferred when small samples are available. The reason why it is only a little
bit slower and not a lot slower as one would imagine is because we are using a closed formula
to calculate the two variance components (Demidenko, 2013, pg. 67-69). Yes, there are closed
formulas for linear mixed models.
Value
For the "varcomps.mom": A vector with 5 elemets, The MSE, the estimate of the between variance,
the variance components ratio and a 95% confidence for the ratio.
For the "varcomps.mle": a list with a single component called "info". That is a matrix with 3
columns, The MSE, the estimate of the between variance and the log-likelihood value. If ranef =
TRUE a list including "info" and an extra component called "ranef" containing the random effects.
It is a matrix with the same number of columns as the data. Each column contains the randome
effects of each variable.
Author(s)
Michail Tsagris and Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Multi-sample tests for vectors
183
References
D.C. Montgomery (2001). Design and analysis of experiments (5th Edition). New York: John
Wiley \& Sons.
Charles S. Davis (2002). Statistical methods for the analysis of repeated measures. New York:
Springer-Verlag.
Demidenko E. (2013). Mixed Models: Theory and Applications with R 2nd Edition). New Jersey:
John Wiley \& Sons (Excellent book).
See Also
colvarcomps.mle, rint.reg, rint.regbx
Examples
## example from Montgomery, pages 514-517
x <- c(98,97,99,96,91,90,93,92,96,95,97,95,95,96,99,98)
ina <- rep(1:4, each = 4)
varcomps.mom(x, ina)
varcomps.mle(x, ina)
Multi-sample tests for vectors
Multi-sample tests for vectors
Description
Multi-sample tests for vectors.
Usage
ftest(x, ina, logged = FALSE)
anova1(x, ina, logged = FALSE)
kruskaltest(x, ina, logged = FALSE)
var2test(x, y, alternative = "unequal", logged = FALSE)
mcnemar(x, y, logged = FALSE)
ttest2(x, y, paired = FALSE, logged = FALSE)
cqtest(x, treat, block, logged = FALSE)
block.anova(x, treat, block, logged = FALSE)
twoway.anova(y, x1, x2, interact = FALSE, logged = FALSE)
Arguments
x
A numerical vector with the data.
y
A numerical vector with the data.
ina
A numerical vector with 1s, 2s, 3s and so one indicating the two groups. Be careful, the function is desinged to accept numbers greater than zero. Alternatively
it can be a factor variable.
184
Multi-sample tests for vectors
paired
This is for the two sample t-test only and is TRUE or FALSE specifying whether
the two samples are paired or not.
alternative
This can either be "unequal", "greater" or "less".
treat
In the case of the blocking ANOVA and Cochran’s Q test, this argument plays
the role of the "ina" argument.
block
This item (in the blocking ANOVA and Cochran’s Q test) denotes the subjects
which are the same. Similarly to "ina" a numeric vector with 1s, 2s, 3s and so
on.
x1
The first factor in the two way ANOVA.
x2
The second factor in the two way ANOVA. The orderis not important.
interact
Should interaction in the two way ANOVA be included? The default value is
FALSE (no interaction).
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
The Welch’s F-test (without assuming equal variances) is performed with the "ftest" function. The
"anova" function perform the classical (Fisher’s) one-way analysis of variance (ANOVA) which
assumes equal variance across the groups. The "kruskaltest" performs the Kruskal-Wallis non parametric alternative to analysis of variance test. The "var2tests" implement the classical F test for the
equality of two sample variances. The "cqtest" performs the Cocrhan’s Q test for the equality of
more than two groups whose values are strictly binary (0 or 1). This is a generalisation of the McNemar’s test in the multi-sample case. The "block.anova" is the ANOVA with blocking, randomised
complete block design (RCBD). In this case, for every combination of the block and treatment values, there is only one observation. The mathematics are the same as in the case of "twoway.anova",
but the assumptions different and the testing procedure also different. In addition, no interaction is
present.
Value
A vector with the test statistic and the p-value of each test. For the case of t-test, an extra column
with the degrees of freedom is given. For the two way ANOVA there can can be either 2 or three F
test statistics and hence the same number of p-values.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
B.L. Welch (1951). On the comparison of several mean values: an alternative approach. Biometrika,
38(3/4), 330-336.
D.C. Montgomery (2001). Design and analysis of experiments (5th Edition). New York: John
Wiley \& Sons.
185
Multinomial regression
McNemar Q. (1947). Note on the sampling error of the difference between correlated proportions
or percentages. Psychometrika. 12(2):153-157.
See Also
ttests, ftests
Examples
x <- rnorm(200)
ina <- rbinom(200, 3, 0.5) + 1
anova1(x, ina)
ftest(x, ina)
ina <- rbinom(200, 1, 0.5) + 1
x1 <- x[ ina == 1 ]
; x2 <- x[ ina == 2 ]
ttest2(x1, x2)
var2test(x1, x2)
## RCBD example 4.1 from Montgomery (2001), page 131-132
x <- c(9.3, 9.4, 9.2, 9.7, 9.4, 9.3, 9.4, 9.6, 9.6, 9.8, 9.5, 10,
10, 9.9, 9.7, 10.2)
tr <- rep(1:4, 4)
bl <- rep(1:4, each = 4)
block.anova(x, tr, bl)
Multinomial regression
Multinomial regression
Description
Multinomial regression.
Usage
multinom.reg(y, x, tol = 1e-07, maxiters = 50)
Arguments
y
The response variable. A numerical or a factor type vector.
x
A matrix or a data.frame with the predictor variables.
tol
This tolerance value to terminate the Newton-Raphson algorithm.
maxiters
The maximum number of iterations Newton-Raphson will perform.
186
Multivariate kurtosis
Value
A list including:
iters
The number of iterations required by the Newton-Raphson.
loglik
The value of the maximised log-likelihood.
be
A matrix with the estimated regression coefficients.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Bohning, D. (1992). Multinomial logistic regression algorithm. Annals of the Institute of Statistical
Mathematics, 44(1): 197-200.
See Also
glm_logistic, score.multinomregs logistic_only
Examples
y <- iris[, 5]
x <- matrnorm(150, 3)
multinom.reg(y, x)
Multivariate kurtosis Multivariate kurtosis
Description
Multivariate kurtosis.
Usage
mvkurtosis(x)
Arguments
x
A numerical matrix.
Details
The multivariate kurtosis is calcualted.
Multivariate Laplace random values simulation
187
Value
A number, the multivariate kurtosis.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>.
References
K. V. Mardia (1970). Measures of Multivariate Skewness and Kurtosis with Applications Biometrika,
57(3):519-530.
See Also
colskewness, skew.test2, colmeans, colVars, colMedians
Examples
x <- as.matrix(iris[, 1:4])
mvkurtosis(x)
Multivariate Laplace random values simulation
Multivariate Laplace random values simulation
Description
Multivariate Laplace random values simulation.
Usage
rmvlaplace(n, lam, mu, G)
Arguments
n
The sample size, a numerical value.
lam
The the parameter of the exponential distribution, a positive number.
mu
The mean vector.
G
A d × d covariance matrix with determinant 1.
Details
The algorithm uses univariate normal random values and transforms them to multivariate via a
spectral decomposition.
188
Multivariate normal and t random values simulation
Value
A matrix with the simulated data.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Eltoft T., Kim T., and Lee T.W. (2006). On the multivariate laplace distribution. Signal Processing
Letters, IEEE, 13(5):300-303.
See Also
rmvnorm, racg, rmvt
Examples
m <- colmeans( as.matrix( iris[, 1:4] ) )
s <- cov(iris[,1:4])
s <- s / det(s)^0.25
lam <- 3
x <- rmvlaplace(100, lam, m, s)
Multivariate normal and t random values simulation
Multivariate normal and t random values simulation
Description
Multivariate normal and t random values simulation.
Usage
rmvnorm(n, mu, sigma)
rmvt(n, mu, sigma, v)
Arguments
n
The sample size, a numerical value.
mu
The mean vector in Rd .
sigma
The covariance matrix in Rd .
v
The degrees of freedom.
Naive Bayes classifiers
189
Details
The algorithm uses univariate normal random values and transforms them to multivariate via a
spectral decomposition. It is faster than the command "mvrnorm" available from MASS, and it
allows for singular covariance matrices.
Value
A matrix with the simulated data.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.
See Also
racg, rmvlaplace, rmvt
Examples
x <- as.matrix(iris[, 1:4])
m <- colmeans(x)
s <- cov(x)
y <- rmvnorm(1000, m, s)
colmeans(y)
cov(y)
y <- NULL
Naive Bayes classifiers
Naive Bayes classifiers
Description
Gaussian, Poisson, geometric and multinomial naive Bayes classifiers.
Usage
gaussian.nb(xnew = NULL, x, ina)
poisson.nb(xnew, x, ina)
multinom.nb(xnew, x, ina)
geom.nb(xnew, x, ina, type = 1)
gammanb(xnew = NULL, x, ina, tol = 1e-07)
190
Naive Bayes classifiers
Arguments
xnew
A numerical matrix with new predictor variables whose group is to be predicted.
For the Gaussian naive Bayes, this is set to NUUL, as you might want just the
model and not to predict the membership of new observations. For the Gaussian
case this contains any numbers, but for the multinomial and Poisson cases, the
matrix must contain integer valued numbers only.
x
A numerical matrix with the observed predictor variable values. For the Gaussian case this contains any numbers, but for the multinomial and Poisson cases,
the matrix must contain integer valued numbers only.
ina
A numerical vector with strictly positive numbers, i.e. 1,2,3 indicating the
groups of the dataset. Alternatively this can be a factor variable.
type
Type 1 refers to the case where the minimum is zero and type 2 for the case of
the minimum being 1. This is for the geometric distribution. This argument is
for the geometric distribution. Type 1 refers to the case where the minimum is
zero and type 2 for the case of the minimum being 1.
tol
The tolerance value to terminate the Newton-Raphson algorithm in the gamma
distribution.
Value
For the Poisson and Multinomial naive Bayes classifiers the estimated group, a numerical vector
with 1, 2, 3 and so on. For the Gaussian naive Bayes classifier a list including:
mu
A matrix with the mean vector of each group based on the dataset.
sigma
A matrix with the variance of each group and variable based on the dataset.
ni
The sample size of each group in the dataset.
est
The estimated group of the xnew observations. It returns a numerical value back
regardless of the target variable being numerical as well or factor. Hence, it is
suggested that you do \"as.numeric(target)\" in order to see what is the predicted
class of the new data.
For the Gamma classifier a list including:
a
A matrix with the shape parameters.
b
A matrix with the scale parameters.
est
The estimated group of the xnew observations. It returns a numerical value back
regardless of the target variable being numerical as well or factor. Hence, it is
suggested that you do \"as.numeric(target)\" in order to see what is the predicted
class of the new data.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Natural Logarithm each element of a matrix
191
See Also
colmeans, colVars
Examples
x <- as.matrix(iris[, 1:4])
a <- gaussian.nb(x, x, iris[, 5])
x1 <- matrix( rpois(100 * 4, 5), ncol = 4)
x2 <- matrix( rpois(50 * 4, 10), ncol = 4)
x <- rbind(x1, x2)
ina <- c( rep(1, 100), rep(2, 50) )
poisson.nb(x, x, ina)
geom.nb(x, x, ina)
multinom.nb(x, x, ina)
Natural Logarithm each element of a matrix
Natural Logarithm each element of a matrix
Description
Natural Logarithm each element of a matrix.
Usage
Log(x, na.rm = FALSE)
Arguments
x
A matrix with data.
na.rm
A boolean value (TRUE/FALSE) for removing NA.
Details
The argument must be a matrix. For vector the time was the same as R’s "log" function so we did
not add it.
Value
A matrix where each element is the natural logarithm of the given argument.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
192
Natural logarithm of the beta function
See Also
Lbeta, Lchoose, Choose
Examples
x <-matrix( runif( 100 * 100), ncol = 100 )
a <- log(x)
b <- Log(x)
all.equal(a, b) # true
x<-a<-b<-NULL
Natural logarithm of the beta function
Natural logarithm of the beta function
Description
Natural logarithm of the beta function.
Usage
Lbeta(x, y)
Arguments
x
A numerical matrix, or a vector or just a number with positive numbers in either
case.
y
A numerical matrix, or a vector or just a number with positive numbers in either
case. The dimensions of y must match those of x.
Details
The function is faster than R’s lbeta when the dimensions of x any are large. If you have only two
numbers, then lbeta is faster. But if you have for example two vectors of 1000 values each, Lbeta
becomes two times faster than lbeta.
Value
The matrix, vector or number with the resulting values.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
Natural logarithm of the gamma function and its derivatives
193
References
Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions. New York: Dover.
https://en.wikipedia.org/wiki/Abramowitz_and_Stegun provides links to the full text which is in
public domain. Chapter 6: Gamma and Related Functions.
See Also
Lgamma, beta.mle, diri.nr2
Examples
x <- rexp(1000)
y <- rexp(1000)
a1 <- Lbeta(x, y)
x<-y<-a1<-NULL
Natural logarithm of the gamma function and its derivatives
Natural logarithm of the gamma function and its derivatives.
Description
Natural logarithm of the gamma function and its derivatives.
Usage
Lgamma(x)
Digamma(x)
Trigamma(x)
Arguments
x
A numerical matrix or vector with positive numbers in either case.
Details
We have spotted that the time savings come when there are more than 50 elements, with vector or
matrix.
Value
The matrix or the vector with the resulting values.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
194
Norm of a matrix
References
Abramowitz, M. and Stegun, I. A. (1972) Handbook of Mathematical Functions. New York: Dover.
https://en.wikipedia.org/wiki/Abramowitz_and_Stegun provides links to the full text which is in
public domain. Chapter 6: Gamma and Related Functions.
See Also
beta.mle, diri.nr2
Examples
x <- matrix( rnorm(500 * 500), ncol = 500 )
a1 <- Lgamma(x)
a2 <- lgamma(x)
all.equal(as.vector(a1), as.vector(a2))
a1 <- Digamma(x)
a2 <- digamma(x)
all.equal(as.vector(a1), as.vector(a2))
x<-a1<-a2<-NULL
Norm of a matrix
Norm of a matrix
Description
Norm of a matrix.
Usage
Norm(x, type = "F")
Arguments
x
type
A matrix with numbers.
The type of norm to be calculated. The default is "F" standing for Frobenius
norm ("f" in R’s norm). The other options are "C" standing for the one norm
("o" in R’s norm), "R" for the identiy norm ("I" in R’s norm) and "M" for the
maximum modulus among elements of a matrix ("M" in R’s norm)
Value
A number, the norm of the matrix.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
Number of equal columns between two matrices
195
See Also
Dist, dista, colmeans
Examples
x <- matrix( rnorm(10 * 10), ncol = 10 )
Norm(x, "F")
norm(x, "F")
Norm(x, "M")
norm(x, "M")
Number of equal columns between two matrices
Number of equal columns between two matrices
Description
Number of equal columns between two matrices.
Usage
mat.mat(x, y)
Arguments
x
A numerical matrix. See details for more information. It must have the same
number of rows as y.
y
A numerical matrix. See details for more information. It must have the same
number of rows as x.
Details
The function takes each column of x and checks the number of times it matches a column of y. In
the example below, we take the first 3 columns of iris as the x matrix. The y matrix is the whole of
iris. We will see how many times, each column of x appears in the y matrix. The answer is 1 for
each column.
Value
A numerical vector of size equal to the number of columns of x.
Author(s)
Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
196
Odds ratio and relative risk
See Also
Match, colmeans, colMedians
Examples
x <- as.matrix(iris[, 1:3])
y <- iris
y[, 5] <- as.numeric(y[, 5])
y <- as.matrix(y)
mat.mat(x, y)
x<-y<-NULL
Odds ratio and relative risk
Odds ratio and relative risk
Description
Odds ratio and relative risk.
Usage
odds.ratio(x, a = 0.05, logged = FALSE)
rel.risk(x, a = 0.05, logged = FALSE)
Arguments
x
A 2 x 2 matrix or a vector with 4 elements. In the case of the vector make sure
it corresponds to the correct table.
a
The significance level, set to 0.05 by default.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
The odds ratio and the confidence interval are calculated.
Value
A list including:
res
The estimated odds ratio and the p-value for the null hypothesis test that it is
equal to 1.
ci
The (1-a)% confidence interval for the true value of the odds ratio.
One sample empirical and exponential empirical likelihood test
197
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Giorgos Athineou <athineou@csd.uoc.gr>
References
Mosteller Frederick (1968). Association and Estimation in Contingency Tables. Journal of the
American Statistical Association. 63(321):1-28.
Edwards A.W.F. (1963). The measure of association in a 2x2 table. Journal of the Royal Statistical
Society, Series A. 126(1):109-114.
See Also
odds, g2Test
Examples
x <- rpois(4, 30)+2
odds.ratio(x)
odds.ratio( matrix(x, ncol = 2) )
One sample empirical and exponential empirical likelihood test
One sample exponential empirical likelihood test
Description
One sample exponential empirical likelihood test.
Usage
eel.test1(x, mu, tol = 1e-09, logged = FALSE)
el.test1(x, mu, tol = 1e-07, logged = FALSE)
Arguments
x
A numerical vector.
mu
The hypothesised mean value.
tol
The tolerance value to stop the iterations of the Newton-Raphson.
logged
Should the logarithm of the p-value be returned? TRUE or FALSE.
198
One sample t-test for a vector
Details
Exponential empirical likelihood is a non parametric method. In this case we use it as the non
parametric alternative to the t-test. Newton-Raphson is used to maximise the log-likelihood ratio
test statistic. In the case of no solution, NULL is returned. Despite the function having beeen
written in R, it is pretty fast. As for the empirical likelihood ratio test, there is a condition for the
range of possible values of mu. If mu is outside this range it is rejected immediately.
Value
iters
The number of iterations required by the Newton-Raphson algorithm. If no covnergence occured this is NULL. This is not returned for the empircial likelihood
ratio test.
info
A vector with three elements, the value of the λ, the likelihood ratio test statistic
and the relevant p-value. If no convergence occured, the value of the λ before is
becomes NA, the value of test statistic is 105 and the p-value is 0. No convergence can be interpreted as rejection of the hypothesis test.
p
The estimated probabilities, one for each observation. If no covnergence occured this is NULL.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Owen A. B. (2001). Empirical likelihood. Chapman and Hall/CRC Press.
See Also
ftest, ttest1
Examples
x <- rnorm(500)
system.time(a1 <- eel.test1(x, 0) )
system.time(a2 <- el.test1(x, 0) )
One sample t-test for a vector
One sample t-test for a vector
Description
One sample t-test for a vector.
One sample t-test for a vector
199
Usage
ttest1(x, m, alternative = "unequal", logged = FALSE, conf = NULL)
Arguments
x
A numerical vector with the data.
m
The mean value under the null hypothesis.
alternative
The alternative hypothesis, "unequal", "greater" or "less".
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
conf
If you want a confidence interval supply the confidence level.
Details
The usual one sample t-test is implemented, only faster.
Value
A list including:
res
A two valued vector with the test statistic and its (logged) p-value.
ci
In the case you supplied a number in the input argument "conf" the relevant
confidence interval will be returned as well.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
See Also
ttest, anova1, ttests
Examples
x = rnorm(500)
t.test(x, mu = 0)
ttest1(x, 0, conf = 0.95)
200
Operations between two matrices or matrix and vector
Operations between two matrices or matrix and vector
Operations between two matrices or matrix and vector
Description
Operations between two matrices or matrix and vector.
Usage
XopY.sum(x, y = NULL, oper = "*")
eachrow(x,y,oper = "*",method = NULL)
eachcol.apply(x,y,indices = NULL,oper = "*",apply = "sum")
Arguments
x
A numerical matrix.
y
A second numerical matrix for "XopY.sum" whose dimensions must match the
ones of x, or vector for "eachrow","eachcol.apply" whose length must match
with the rows of x.
oper
The operation to be performed, either "*", "/", "+" or "-".
method
A character value for choosing option to apply in the result. Options: 1) sum 2)
max 3) min
indices
An integer vector with indices to specific columns. Only for "eachcol.apply".
apply
A character value with the function to be applied in the columns of the matrix.
Only for "eachcol.apply". Options: 1) sum 2) median 3) max 4) min
Details
XopY.sum: sum(X op Y) where op can be on of "+,-,*,/".
eachrow: X op Y by row or FUNCTION(X op Y) where "x" is matrix, "y" is vector with length as
much an the columns of x and "op" is one of "+,-,*,/", and "FUNCTION" is a specific method for
applying in the result matrix (see argument method).
eachcol.apply: FUNCTION(X op Y) by column where "x" is matrix, "y" is vector with length as
much an the rows of x, "op" is one of "+,-,*,/" and "FUNCTION" is a specific method (see argument
apply).
Value
XopY.sum: sum(X op Y) where "op" can be on of "+,-,*,/".
eachrow: operation by row between a matrix and a vector."op" can be on of "+,-,*,/". If "suma=TRUE"
then returns the sum of this operation.
eachcol.apply: operation by column between a matrix and a vector and applied a specific function."op" can be on of "+,-,*,/".
Orthogonal matching pursuit regression
201
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
Dist, dista, colmeans, Diag.fill,colMads, rowMads
Examples
x <- matrix( rnorm(5 * 5), ncol = 5 )
y <- matrix( rnorm(5 * 5), ncol = 5 )
XopY.sum(x, y, oper = "*")
y <- x[,1]
eachrow(x,y)
all.equal(eachcol.apply(x,y),colsums(x*y))
x<-y<-NULL
Orthogonal matching pursuit regression
Orthogonal matching pursuit regression
Description
Orthogonal matching pursuit regression.
Usage
ompr(y, x, method = "BIC", tol = 2 )
omp(y, x, tol = qchisq(0.95, 1) + log( length(y) ), type = "logistic" )
Arguments
y
x
method
tol
The response variable, a numeric vector. For "ompr" this is a continuous variable. For "omp" this can be either a vector with discrete (count) data, 0 and 1,
non negative values, strictly positive or proportions including 0 and 1.
A matrix with the data, where the rows denote the samples and the columns are
the variables.
You can choose between the change in the BIC ("BIC"), the adjusted R2 or the
SSE ("SSE").
The tolerance value to terminate the algorithm. This is the change in the criterion
value between two successive steps. For "ompr" the default value is 2 because
the default method is "BIC". For "omp" the default value is the 95% quantile of
the χ2 distribution with 1 degree of freedom plus the logarithm of the sample
size.
202
Permutation
type
This denotes the parametric model to be used each time. It depends upon the
nature of y. The possible values are "logistic", "poisson", "quasipoisson", "quasibinomial", "normlog", "weibull", or "mv" (for multivariate response variable).
Value
A matrix with two columns. The selected variable(s) and the criterion value at every step.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>.
References
Pati Y. C., Rezaiifar R. & Krishnaprasad P. S. (1993). Orthogonal matching pursuit: Recursive
function approximation with applications to wavelet decomposition. In Signals, Systems and Computers. 1993 Conference Record of The Twenty-Seventh Asilomar Conference on. IEEE.
Mazin Abdulrasool Hameed (2012). Comparative analysis of orthogonal matching pursuit and least
angle regression. MSc thesis, Michigan State University. https://www.google.gr/url?sa=t&rct=j&q=&esrc=s&source=web&c
Lozano A., Swirszcz G., & Abe N. (2011). Group orthogonal matching pursuit for logistic regression. In Proceedings of the Fourteenth International Conference on Artificial Intelligence and
Statistics.
See Also
cor.fbed, cor.fsreg, correls, fs.reg
Examples
x
y
a
a
x
<- matrnorm(100, 400)
<- rnorm(100)
<- ompr(y, x)
<- NULL
Permutation
Permutation
Description
Permute the given vector.
Usage
permutation(x, nperm = gamma(length(x)+1))
permutation.next(x, nperm = gamma(length(x)+1))
permutation.prev(x, nperm = gamma(length(x)+1))
bincomb(n)
Permutation based p-value for the Pearson correlation coefficient
203
Arguments
x
A numeric vector with data.
nperm
An integer value for returning specific number of combinations. By defualt is
set to all combinations. Must be between 0<=nperm<=gamma(length(x)+1)
n
An integer value for the length of the binary number.
Details
This function implements "Permutation", which means all the possible combinations. In the permutation.next and permutation.prev if there aren’t possible combinations it returns the same vector.
"Binary Combinations" for "bincomb", means all the possible combinations for the binary number
with length "n".
Value
Returns a matrix with all possible combinations of the given vector or a matrix row with one possible
combinations.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
See Also
combn,comb_n
Examples
y
b
b
b
g
<<<<<-
rnorm(3)
permutation(y)
permutation.next(y)
permutation.prev(y)
bincomb(3)
Permutation based p-value for the Pearson correlation coefficient
Permutation based p-value for the Pearson correlation coefficient
Description
Permutation based p-value for the Pearson correlation coefficient.
Usage
permcor(x, y, R = 999)
204
Prediction with some naive Bayes classifiers
Arguments
x
A numerical vector with the first variable.
y
A numerical vector with the second variable.
R
The number of permutations to be conducted; set to 999 by default.
Details
This is a very low computational calculation of the p-value. Try it yourselves.
Value
A vector consisting of two values, the Pearson correlation and the permutation based p-value.
Author(s)
Marios Dimitriadis and Michail Tsagris
R implementation and documentation: Marios Dimitriadis and Michail Tsagris <kmdimitriadis@gmail.com>
and <mtsagris@csd.uoc.gr>
See Also
pc.skel
Examples
x <- iris[, 1]
y <- iris[, 2]
permcor(x, y)
permcor(x, y, R = 9999)
Prediction with some naive Bayes classifiers
Prediction with some naive Bayes classifiers
Description
Prediction with some naive Bayes classifiers.
Usage
gaussiannb.pred(xnew, m, s, ni)
poissonnb.pred(xnew, m)
multinomnb.pred(xnew, m)
gammanb.pred(xnew, a, b)
geomnb.pred(xnew, prob)
Quasi binomial regression for proportions
205
Arguments
xnew
A numerical matrix with new predictor variables whose group is to be predicted.
For the Gaussian case this contains any numbers, but for the multinomial and
Poisson cases, the matrix must contain integer valued numbers only.
m
A matrix with the group means. Each row corresponds to a group.
s
A matrix with the group colum-wise variances. Each row corresponds to a
group.
ni
A vector with the frequencies of each group.
a
A vector with the shape parameters of each group.
b
A vector with the scale parameters of each group.
prob
A vector with the sprobability parameters of each group.
Value
A numerical vector with 1, 2, ... denoting the predicted group.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
gaussian.nb, colpoisson.mle colVars
Examples
ina <- sample(1:150, 100)
x <- as.matrix(iris[, 1:4])
id <- as.numeric(iris[, 5])
a <- gaussian.nb(xnew = NULL, x[ina, ], id[ina])
est <- gaussiannb.pred(x[-ina, ], a$mu, a$sigma, a$ni)
table(id[-ina], est)
Quasi binomial regression for proportions
Quasi binomial regression for proportions
Description
Quasi binomial regression for proportions.
206
Quasi binomial regression for proportions
Usage
prop.reg(y, x, varb = "quasi", tol = 1e-09, maxiters = 100)
prop.regs(y, x, varb = "quasi", tol = 1e-09, logged = FALSE, maxiters = 100)
Arguments
y
A numerical vector proportions. 0s and 1s are allowed.
x
For the "prop.reg" a matrix with data, the predictor variables. This can be a
matrix or a data frame. For the "prop.regs" this must be a numerical matrix,
where each columns denotes a variable.
tol
The tolerance value to terminate the Newton-Raphson algorithm. This is set to
10−9 by default.
varb
The type of estimate to be used in order to estimate the covariance matrix of the
regression coefficients. There are two options, either "quasi" (default value) or
"glm". See the references for more information.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
maxiters
The maximum number of iterations before the Newton-Raphson is terminated
automatically.
Details
We are using the Newton-Raphson, but unlike R’s built-in function "glm" we do no checks and no
extra calculations, or whatever. Simply the model. The "prop.regs" is to be used for very many
univariate regressions. The "x" is a matrix in this case and the significance of each variable (column
of the matrix) is tested. The function accepts binary responses as well (0 or 1).
Value
For the "prop.reg" function a list including:
iters
The number of iterations required by the Newton-Raphson.
varb
The covariance matrix of the regression coefficients.
phi
The phi parameter is returned if the input argument "varb" was set to "glm",
othwerise this is NULL.
info
A table similar to the one produced by "glm" with the estimated regression coefficients, their standard error, Wald test statistic and p-values.
For the "prop.regs" a two-column matrix with the test statistics (Wald statistic) and the associated
p-values (or their loggarithm).
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Quasi Poisson regression for count data
207
References
Papke L. E. & Wooldridge J. (1996). Econometric methods for fractional response variables with an
application to 401(K) plan participation rates. Journal of Applied Econometrics, 11(6): 619–632.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
anova_propreg univglms, score.glms, logistic_only
Examples
y <- rbeta(100, 1, 4)
x <- matrix(rnorm(100 * 3), ncol = 3)
a <- prop.reg(y, x)
y <- rbeta(100, 1, 4)
x <- matrix(rnorm(400 * 100), ncol = 400)
b <- prop.regs(y, x)
mean(b[, 2] < 0.05)
Quasi Poisson regression for count data
Quasi Poisson regression
Description
Quasi Poisson regression.
Usage
qpois.reg(x, y, full = FALSE, tol = 1e-09,maxiters = 100)
qpois.regs(x, y, tol = 1e-09, logged = FALSE)
Arguments
x
For the "qpois.reg" a matrix with data, the predictor variables. This can be a
matrix or a data frame. For the "qpois.regs" this must be a numerical matrix,
where each columns denotes a variable.
y
A numerical vector with positive discrete data.
full
If this is FALSE, the coefficients, the deviance and the estimated phi parameter
will be returned only. If this is TRUE, more information is returned.
tol
The tolerance value to terminate the Newton-Raphson algorithm. This is set to
10−9 by default.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
maxiters
The maximum number of iterations before the Newton-Raphson is terminated
automatically.
208
Quasi Poisson regression for count data
Details
We are using the Newton-Raphson, but unlike R’s built-in function "glm" we do no checks and no
extra calculations, or whatever. Simply the model, unless the user requests for the Wald tests of
the coefficients. The "qpois.regs" is to be used for very many univariate regressions. The "x" is a
matrix in this case and the significance of each variable (column of the matrix) is tested.
Value
For the "prop.reg" a list including: When full is FALSE
be
The regression coefficients.
devi
The deviance of the model.
varb
The covariance matrix of the beta coefficients.
phi
The phi parameter, the estimate of dispersion.
When full is TRUE, the additional item is:
info
The regression coefficients, their standard error, their Wald test statistic and their
p-value.
For the "prop.regs" a two-column matrix with the test statistics (Wald statistic) and the associated
p-values (or their loggarithm).
Author(s)
Manos Papadakis and Marios Dimitriadis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com> and Marios
Dimitriadis <kmdimitriadis@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
prop.reg univglms, score.glms, poisson_only
Examples
y <- rnbinom(100, 10, 0.6)
x <- matrix(rnorm(100*3), ncol = 3)
mod1 <- glm(y ~ x, quasipoisson)
summary(mod1)
qpois.reg(x, y, full = TRUE)
qpois.regs(x, y)
Random intercepts linear mixed models
209
Random intercepts linear mixed models
Random intercepts linear mixed models
Description
Random intercepts linear mixed models (for balanced data with a single identical covariate).
Usage
rint.reg(y, x, id ,tol = 1e-08, ranef = FALSE, maxiters = 100)
rint.regbx(y, x, id)
Arguments
y
x
id
tol
ranef
maxiters
A numerical vector with the data. The subject values.
For the case of "rint.reg" this can be a vector or a numerical matrix with data.
In the case of "rint.regbx" this is a numerical vector with the same length as y
indicating the fixed predictor variable. Its values are the same for all levels of y.
An example of this x is time which is the same for all subjects.
A numerical variable with 1, 2, ... indicating the subject.
The tolerance level to terminate the generalised elast squares algorithm.
If you want to obtain the random effects (random intercepts) set this equal to
TRUE.
The max number of iterations that can take place in a regression.
Details
Random intercepts linear mixed models with compound covariance structure is fitted in both functions. The "rint.reg" allows any numerical matrix, with balanced or unbalanced data. See Demidenko (2013, pg. 65-67) for more information.
The "rint.regbx" is a special case of a balanced random intercepts model with a compound symmetric covariance matrix and one single covariate which is constant for all replicates. An example, is
time, which is the same for all subjects. Maximum likelihood estimation has been performed. In
this case the mathematics exist in a closed formula (Demidenko, 2013, pg. 67-69).
Value
A list including:
info
be
ranef
A vector with the random intercepts variance (between), the variance of the
errors (within), the log-likelihood, the deviance (twice the log-likelihood) and
the BIC. In the case of "rint.reg" it also includes the number of iterations required
by the generalised least squares.
The estimated regression coefficients, which in the case of "rint.regbx" are simply two: the constant and the slope (time effect).
The random intercepts effects.
210
Random values simulation from a von Mises distribution
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Eugene Demidenko (2013). Mixed Models: Theory and Applications with R, 2nd Edition. New
Jersey: Wiley \& Sons (excellent book).
See Also
rm.lines, varcomps.mom, colvarcomps.mom
Examples
y <- rnorm(100)
x <- rnorm(10)
x <- rep(x, 10)
id <- rep(1:10, each = 10)
system.time( for (i in 1:40) a <- rint.reg(y, x, id) )
Random values simulation from a von Mises distribution
Random values simulation from a von Mises distribution
Description
It generates random vectors following the von Mises distribution. The data can be spherical or
hyper-spherical.
Usage
rvonmises(n, m, k, rads = TRUE)
Arguments
n
The sample size.
m
The mean angle expressed in radians or degrees.
k
The concentration parameter. If k is zero the sample will be generated from the
uniform distribution over (0, 2π).
rads
If the mean angle is expressed in radians, this should be TRUE and FALSE
otherwise. The simulated data will be expressed in radians or degrees depending
on what the mean angle is expressed.
Ranks of the values of a vector
211
Details
The mean direction is transformed to the Euclidean coordinates (i.e. unit vector) and then the fvmf
function is employed. It uses a rejection smapling as suggested by Andrew Wood in 1994. I have
mentioned the description of the algorithm as I found it in Dhillon and Sra in 2003. Finally, the data
are transformed to radians or degrees.
Value
A vector with the simulated data.
Author(s)
Michail Tsagris and Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm85@gmail.com>
References
Wood, A. T. (1994). Simulation of the von Mises Fisher distribution. Communications in statisticssimulation and computation, 23(1): 157-164.
Dhillon, I. S., & Sra, S. (2003). Modeling data using directional distributions. Technical Report TR03-06, Department of Computer Sciences, The University of Texas at Austin. http://citeseerx.ist.psu.edu/viewdoc/download?d
See Also
vm.mle, rvmf
Examples
x <- rvonmises(1000, 2, 25, rads = TRUE)
vm.mle(x)
Ranks of the values of a vector
Ranks of the values of a vector
Description
Ranks of the values of a vector.
Usage
Rank(x,method = "average",descending = FALSE,stable = FALSE)
212
Reading the files of a directory
Arguments
x
A numerical vector with data.
method
a character string for choosing method. Must be one of "average", "min", "max",
"first".
descending
A boolean value (TRUE/FALSE) for sorting the vector in descending order. By
default sorts the vector in ascending.
stable
A boolean value (TRUE/FALSE) for choosing a stable sort algorithm. Stable
means that discriminates on the same elements. Only for the method "first".
Details
The ranks of the values are returned, the same job as "rank". If you want you can choose descending/ascending order for all methods. Only for method "first" you can choose for stable sorting but
choose it if you have many duplicates values.
Value
A vector with the ranks of the values.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colRanks, correls
Examples
x <- rnorm(100)
a1 <- Rank(x)
a2 <- rank(x)
Reading the files of a directory
Reading the files of a directory
Description
Reading the files of a directory.
Usage
read.directory(path.directory)
read.examples(path.man,dont.read = "")
Reading the files of a directory
213
Arguments
path.directory The full path to the directory. For example: \"C:\Users\username\Documents\R\Rfast_1.8.0\R\"
path.man
The full path to the directory with the Rd files in it. For example: \"C:\Users\username\Documents\R\Rfast
dont.read
A character vector with the name of the files that you wish not to read. By
default it’s empty \"\".
Details
For function \"read.directory\": Takes as an argument a full path to a directory and returns the names
of the files.
For function \"read.examples\": Takes as an argument a full path to the directory of the Rd files and
the name of the files that shouldn’t read.
Value
For function \"read.directory\": The names of the files.
For function \"read.examples\": a list with 2 fields
examples
A character vector with the examples of each Rd file.
files
A character vector with the name of the file that each examples belongs.
long_lines
A character vector with the name of the file that has large examples.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
AddToNamespace, sourceR, sourceRd, checkRd, checkExamples
Examples
# for example: path="C:\some_file\"
# system.time( read.directory(path) )
# system.time( list.dirs(path) )
# for example: path.man="C:\some_file\man\"
# system.time( read.examples(path.man) )
# system.time( read.examples(path.man,dont.read=c("somef_1.Rd",...,"somef_n.Rd") ) )
214
Repeated measures anova
Repeated measures anova
Repeated measures anova
Description
Repeated measures anova.
Usage
rm.anova(y, logged = FALSE)
Arguments
y
A matrix with the data, where each column refers to a different measurement.
The rows denote the subjects.
logged
Should the p-values be returned (FALSE) or their logarithm (TRUE)?
Details
Found in Davis (2002) is the usual repeated measures ANOVA. In this case, suppose you have taken
measurements on one or more variables from the same group of people. See the example below on
how to put such data.
Value
A vector with the test statistic (t-test) and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Charles S. Davis (2002). Statistical methods for the analysis of repeated measures. Springer-Verlag,
New York.
See Also
rm.anovas, rint.reg, varcomps.mle
215
Replicate columns/rows
Examples
y <- c(74.5,81.5,83.6,68.6,73.1,79.4,
75.5,84.6,70.6,87.3,73.0,75.0,
68.9,71.6,55.9,61.9,60.5,61.8,
57.0,61.3,54.1,59.2,56.6,58.8,
78.3,84.9,64.0,62.2,60.1,78.7,
54.0,62.8,63.0,58.0,56.0,51.5,
72.5,68.3,67.8,71.5,65.0,67.7,
80.8,89.9,83.2,83.0,85.7,79.6)
y <- matrix(y, ncol = 6, byrow = TRUE)
rm.anova(y)
Replicate columns/rows
Replicate columns/rows
Description
Replicate columns/rows.
Usage
rep_col(x,n)
rep_row(x,n)
Arguments
x
A vector with data.
n
Number of new columns/rows.
Value
A matrix where each column/row is equal to "x".
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, rowFalse, nth, colrange, colMedians, colVars, sort_mat, rowTrue
Examples
x <- runif(10)
all.equal(rep_col(x,10),matrix(x,nrow=length(x),ncol=10))
all.equal(rep_row(x,10),matrix(x,ncol=length(x),nrow=10,byrow=TRUE))
216
Round each element of a matrix/vector
Round each element of a matrix/vector
Round each element of a matrix/vector
Description
Round each element of a matrix/vector.
Usage
Round(x,digit=0,na.rm = FALSE)
Arguments
x
A numeric matrix/vector with data or NA. NOT integer values.
digit
An integer value for 0...N-1 where N is the number of the digits. By default is 0.
na.rm
TRUE or FAlSE for remove NAs if exists.
Details
Round is a very fast C++ implementation. Especially for large data. It handles NA.
Value
A vector/matrix where each element is been rounded in the given digit.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
Lchoose, Log, Choose
Examples
x <-matrix( rnorm( 500 * 100), ncol = 100 )
system.time( a <- Round(x,5) )
system.time( b <- round(x,5) )
all.equal(a,b) #true
x <-rnorm( 1000)
system.time( a <- Round(x,5) )
system.time( b <- round(x,5) )
all.equal(a,b) # true
Row - Wise matrix/vector count the frequency of a value
217
Row - Wise matrix/vector count the frequency of a value
Row - Wise matrix/vector count the frequency of a value
Description
Row - Wise matrix/vector count the frequency of a value.
Usage
count_value(x, value)
colCountValues(x, values, parallel = FALSE)
rowCountValues(x, values, parallel = FALSE)
countNA(x)
Arguments
x
A vector with the data (numeric or character) or a numeric matrix.
value
The value, numeric or NA, to check its frequency in the vector "x".
values
a vector with the values to check its frequency in the matrix "x" by row or column.
parallel
Do you want to do it in parallel in C++? TRUE or FALSE. Works with every
other argument.
Details
The functions is written in C++ in order to be as fast as possible. The "x" and "value" must have
the same type. The type can be numeric or character.
Value
The frequency of a value/values in a vector in linear time or by row/column in a matrix.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
med, binary_search, Order, nth
218
Row-wise minimum and maximum
Examples
x <- rnorm(100)
value <- x[50]
system.time( count_value(x,value) )
countNA(x)
y <- sample(letters,replace=TRUE)
value <- "r"
system.time( count_value(y,value) )
values <- sample(x,100,replace=TRUE)
x <- matrix(x,100,100)
colCountValues(x,values)
rowCountValues(x,values)
x<-value<-values<-y<-NULL
Row-wise minimum and maximum
Row-wise minimum and maximum of a matrix.
Description
Row-wise minimum and maximum of a matrix.
Usage
rowMins(x, value = FALSE)
rowMaxs(x, value = FALSE)
rowMinsMaxs(x)
Arguments
x
A numerical matrix with data.
value
If the value is FALSE it returns the indices of the minimum/maximum, otherwise
it returns the minimum and maximum values.
Value
A vector with the relevant values.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colMins, colMaxs, nth, rowrange colMedians, colVars, sort_mat
219
Row-wise true value
Examples
x <- matrix( rnorm(500 * 500), ncol = 500 )
system.time( s1 <- rowMins(x) )
system.time( s2 <- apply(x, 1, min) )
system.time( s1 <- rowMaxs(x) )
system.time( s2 <- apply(x, 1, max) )
system.time( s1 <- c(apply(x, 1, min),apply(x, 1, max) ))
system.time( s2 <- rowMinsMaxs(x) )
x<-s1<-s2<-NULL
Row-wise true value
Row-wise true value of a matrix
Description
Row-wise true value of a matrix.
Usage
rowTrue(x)
rowFalse(x)
rowTrueFalse(x)
Arguments
x
A logical matrix with data.
Value
An integer vector where item "i" is the number of the true/false values of "i" row.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, colFalse, nth, rowrange, rowMedians, rowVars, sort_mat, colTrue
220
Search for variables with zero range in a matrix
Examples
x <- matrix(as.logical(rbinom(100*100,1,0.5)),100,100)
s1 <- rowTrue(x)
s1 <- rowFalse(x)
s1 <- rowTrueFalse(x)
x<-s1<-NULL
Search for variables with zero range in a matrix
Search for variables with zero range in a matrix
Description
Search for variables with zero range in a matrix.
Usage
check_data(x, ina = NULL)
Arguments
x
A matrix or a data.frame with the data, where rows denotes the observations and
the columns contain the dependent variables.
ina
If your data are grouped, for example there is a factor or numerical variable
indicating the groups of the data supply it here, otherwise leave it NULL.
Details
The function identifies the variabels with zero range, instead of a zero variance as this is faster. It
will work with matrices and data.frames.
Value
A numerical vector of length zero if no zero ranged variable exists, or of length at least one with the
index (or indices) of the variable(s) that need attention or need to be removed.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Significance testing for the coefficients of Quasi binomial or the quasi Poisson regression
221
See Also
colrange, colVars
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
check_data(x)
## some variables have a constant value
x[, c(1,10, 50, 70)] <- 1
check_data(x)
id <- rep(1:4, each = 25 )
x[1:25, 2] <- 0
check_data(x) ## did not use the id variable
check_data(x, id) ## see now
x <- NULL
Significance testing for the coefficients of Quasi binomial or the quasi Poisson regression
Significance testing for the coefficients of Quasi binomial or the quasi
Poisson regression
Description
Significance testing for the coefficients of Quasi binomial or the quasi Poisson regression.
Usage
anova_propreg(mod, poia = NULL)
anova_qpois.reg(mod, poia = NULL)
Arguments
mod
poia
An object as returned by the "prop.reg" or the "qpois.reg" function.
If you want to test the significance of a single coefficient this must be a number.
In this case, the "prop.reg" or the "qpois.reg" function contains this information.
If you want more coefficients to be testes simultaneously, e.g. for a categorical
predictor, then this must contain the positions of the coefficients. If you want to
see if all coefficients are zero, like an overall F-test, leave this NULL.
Details
Even though the name of this function starts with anova it is not an ANOVA type significance
testing, but a Wald type.
Value
A vector with three elements, the test statistic value, its associated p-value and the relevant degrees
of freedom.
222
Simulation of random values from a Bingham distribution
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Papke L. E. & Wooldridge J. (1996). Econometric methods for fractional response variables with
an application to 401(K) plan participation rates. Journal of Applied Econometrics, 11(6): 619-632.
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
prop.reg, qpois.reg, univglms, score.glms, logistic_only
Examples
y <- rbeta(1000, 1, 4)
x <- matrix(rnorm(1000 * 3), ncol = 3)
a <- prop.reg(y, x)
## all coefficients are tested
anova_propreg(a)
## the first predictor variable is tested
anova_propreg(a, 2)
a ## this information is already included in the model output
## the first and the second predictor variables are tested
anova_propreg(a, 2:3)
Simulation of random values from a Bingham distribution
Simulating from a Bingham distribution
Description
Simulation from a Bingham distribution using the code suggested by Kent et al. (2013).
Usage
rbing(n, lam)
Arguments
n
Sample size.
lam
Eigenvalues of the diagonal symmetric matrix of the Bingham distribution. See
details for more information on this.
Simulation of random values from a Bingham distribution with any symmetric matrix
223
Details
The user must have calculated the eigenvalues of the diagonal symmetric matrix of the Bingham
distribution. The function accepts the q-1 eigenvalues only. This means, that the user must have subtracted the lowest eigenvalue from the rest and give the non zero ones. The function uses rejection
sampling.
Value
A matrix with the simulated data.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
References
Kent J.T., Ganeiber A.M. and Mardia K.V. (2013). A new method to simulate the Bingham and related distributions in directional data analysis with applications. http://arxiv.org/pdf/1310.8110v1.pdf
C.J. Fallaize and T. Kypraios (2014). Exact Bayesian Inference for the Bingham Distribution.
Statistics and Computing (No volum assigned yet). http://arxiv.org/pdf/1401.2894v1.pdf
See Also
rvmf
Examples
x <- rbing( 100, c(1, 0.6, 0.1) )
x
Simulation of random values from a Bingham distribution with any symmetric matrix
Simulation of random values from a Bingham distribution with any
symmetric matrix
Description
Simulation of random values from a Bingham distribution with any symmetric matrix.
Usage
rbingham(n, A)
224
Simulation of random values from a normal distribution
Arguments
n
Sample size.
A
A symmetric matrix.
Details
The eigenvalues of the q x q symmetric matrix A are calculated and the smallest of them is subtracted from the rest. The q - 1 non zero eiqenvalues are then passed to rbing. The generated data
are then right multiplied by V T , where V is the matrix of eigenvectors of the matrix A.
Value
A matrix with the simulated data.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
References
Kent J.T., Ganeiber A.M. and Mardia K.V. (2013). A new method to simulate the Bingham and related distributions in directional data analysis with applications. http://arxiv.org/pdf/1310.8110v1.pdf
C.J. Fallaize and T. Kypraios (2014). Exact Bayesian Inference for the Bingham Distribution.
Statistics and Computing (No volum assigned yet). http://arxiv.org/pdf/1401.2894v1.pdf
See Also
rvmf
Examples
A <- cov( iris[, 1:4] )
x <- rbingham(100, A)
x
Simulation of random values from a normal distribution
Simulation of random values from a normal distribution
Description
Simulation of random values from a normal distribution.
Simulation of random values from a von Mises-Fisher distribution
225
Usage
Rnorm(n, m = 0, s = 1)
Arguments
n
The sample size.
m
The mean, set to 0 by default.
s
The standard devation, set to 1 by default.
Details
By using the Ziggurat method of generating standard normal variates, this function is really fast
when you want to generate large vectors. For less than 2,000 this might make no difference when
compared with R’s "rnorm", but for 10,000 this will be 6-7 times faster.
Value
A vector with n values.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
See Also
matrnorm, rvonmises, rvmf, rmvnorm
Examples
x <- Rnorm(500)
Simulation of random values from a von Mises-Fisher distribution
Random values simulation from a von Mises-Fisher distribution
Description
It generates random vectors following the von Mises-Fisher distribution. The data can be spherical
or hyper-spherical.
Usage
rvmf(n, mu, k)
226
Simulation of random values from a von Mises-Fisher distribution
Arguments
n
The sample size.
mu
The mean direction, a unit vector.
k
The concentration parameter. If k = 0, random values from the spherical uniform will be drwan. Values from a multivariate normal distribution with zero
mean vector and the identity matrix as the covariance matrix. Then each vector
becomes a unit vector.
Details
It uses a rejection smapling as suggested by Andrew Wood (1994).
Value
A matrix with the simulated data.
Author(s)
Michail Tsagris and Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm85@gmail.com>
References
Wood A. T. A. (1994). Simulation of the von Mises Fisher distribution. Communications in
statistics-simulation and computation, 23(1): 157–164.
Dhillon I. S. & Sra S. (2003). Modeling data using directional distributions. Technical Report TR03-06, Department of Computer Sciences, The University of Texas at Austin. http://citeseerx.ist.psu.edu/viewdoc/download?d
See Also
vmf.mle, rvonmises, iag.mle
Examples
m <- rnorm(4)
m <- m/sqrt(sum(m^2))
x <- rvmf(1000, m, 25)
m
vmf.mle(x)
Skeleton of the PC algorithm
227
Skeleton of the PC algorithm
The skeleton of a Bayesian network produced by the PC algorithm
Description
The skeleton of a Bayesian network produced by the PC algorithm.
Usage
pc.skel(dataset, method = "pearson", alpha = 0.01, R = 1, stat = NULL, ini.pvalue = NULL)
Arguments
dataset
A numerical matrix with the variables. If you have a data.frame (i.e. categorical
data) turn them into a matrix using data.frame.to_matrix. Note, that for
the categorical case data, the numbers must start from 0. No missing data are
allowed.
method
If you have continuous data, you can choose either "pearson" or "spearman". If
you have categorical data though, this must be "cat". In this case, make sure the
minimum value of each variable is zero. The g2Test and the relevant functions
work that way.
alpha
The significance level (suitable values in (0, 1)) for assessing the p-values. Default (preferred) value is 0.01.
R
The number of permutations to be conducted. The p-values are assessed via permutations. Use the default value if you want no permutation based assessment.
stat
If the initial test statistics (univariate associations) are available, pass them through
this parameter.
ini.pvalue
if the initial p-values of the univariate associations are available, pass them
through this parameter.
Details
The PC algorithm as proposed by Spirtes et al. (2000) is implemented. The variables must be either
continuous or categorical, only. The skeleton of the PC algorithm is order independent, since we
are using the third heuristic (Spirte et al., 2000, pg. 90). At every stage of the algorithm use the
pairs which are least statistically associated. The conditioning set consists of variables which are
most statistically associated with each other of the pair of variables.
For example, for the pair (X, Y) there can be two conditioning sets for example (Z1, Z2) and (W1,
W2). All p-values and test statistics and degrees of freedom have been computed at the first step
of the algorithm. Take the p-values between (Z1, Z2) and (X, Y) and between (Z1, Z2) and (X,
Y). The conditioning set with the minimum p-value is used first. If the minimum p-values are the
same, use the second lowest p-value. If the unlikely, but not impossible, event of all p-values being
the same, the test statistic divided by the degrees of freedom is used as a means of choosing which
conditioning set is to be used first.
228
Skeleton of the PC algorithm
If two or more p-values are below the machine epsilon (.Machine$double.eps which is equal to
2.220446e-16), all of them are set to 0. To make the comparison or the ordering feasible we use the
logarithm of p-value. Hence, the logarithm of the p-values is always calculated and used.
In the case of the G2 test of independence (for categorical data) with no permutations, we have
incorporated a rule of thumb. If the number of samples is at least 5 times the number of the parameters to be estimated, the test is performed, otherwise, independence is not rejected according to
Tsamardinos et al. (2006). We have modified it so that it calculates the p-value using permutations.
Value
A list including:
stat
The test statistics of the univariate associations.
ini.pvalue
The initial p-values univariate associations.
pvalue
The logarithm of the p-values of the univariate associations.
runtime
The amount of time it took to run the algorithm.
kappa
The maximum value of k, the maximum cardinality of the conditioning set at
which the algorithm stopped.
n.tests
The number of tests conducted during each k.
G
The adjancency matrix. A value of 1 in G[i, j] appears in G[j, i] also, indicating
that i and j have an edge between them.
sepset
A list with the separating sets for every value of k.
Author(s)
Marios Dimitriadis
R implementation and documentation: Marios Dimitriadis <kmdimitriadis@gmail.com>
References
Spirtes P., Glymour C. and Scheines R. (2001). Causation, Prediction, and Search. The MIT Press,
Cambridge, MA, USA, 3nd edition.
Tsamardinos I., Borboudakis G. (2010) Permutation Testing Improves Bayesian Network Learning.
In Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2010. 322-337.
Tsamardinos I., Brown E.L. and Aliferis F.C. (2006). The max-min hill-climbing Bayesian network
structure learning algorithm. Machine learning 65(1):31-78.
See Also
g2Test, g2Test_univariate, cora, correls
Examples
# simulate a dataset with continuous data
dataset <- matrix(rnorm(1000 * 50, 1, 100), nrow = 1000)
a <- pc.skel(dataset, method = "pearson", alpha = 0.01)
Skewness and kurtosis coefficients
229
Skewness and kurtosis coefficients
Skewness and kurtosis coefficients
Description
Skewness and kurtosis coefficients.
Usage
skew(x, pvalue = FALSE)
kurt(x, pvalue = FALSE)
Arguments
x
A numerical vector with data.
pvalue
If you want a hypothesis test that the skewness or kurtosis are significant set this
to TRUE. This checks whether the skewness is significantly different from 0 and
whether the kurtosis is significantly different from 3.
Details
The sample skewness and kurtosis coefficient are calculated. For the kurtosis we do not subtract 3.
Value
If "pvalue" is FALSE (default value) the skewness or kurtosis coefficients are returned. Otherwise,
the p-value of the significance of the coefficient is returned.
Author(s)
Klio Lakiotaki
R implementation and documentation: Klio Lakiotaki <kliolak@gmail.com>.
References
https://en.wikipedia.org/wiki/Skewness
https://en.wikipedia.org/wiki/Kurtosis
See Also
colskewness, skew.test2, colmeans, colVars, colMedians
230
Some summary statistics of a vector for each level of a grouping variable
Examples
x <- rgamma(500,1, 4)
skew(x)
kurt(x, TRUE)
Some summary statistics of a vector for each level of a grouping variable
Some summary statistics of a vector for each level of a grouping variable.
Description
Some summary statistics of a vector for each level of a grouping variable.
Usage
group.var(x, ina,ina.max = max(ina))
group.all(x, ina,ina.max = max(ina))
group.any(x, ina,ina.max = max(ina))
group.mad(x, ina,method = "median")
group.mean(x, ina,ina.max = max(ina))
group.med(x, ina)
group.min(x, ina,ina.max = max(ina))
group.max(x, ina,ina.min = NULL,ina.max = NULL)
group.min_max(x, ina,ina.max = max(ina))
Arguments
x
A numerical vector with data.
ina
A numerical vector or a factor variable. For every distinct value of "ina" the
variance (or standard deviation) of "x" will be calculated. Note that negative
values are not allowed as this can cause R to run forever or crash.
method
A character vector with values "median", for median absolute deviation or "mean",
for mean absolute deviation.
ina.max
Maximum number for vector ina.
ina.min
Minimum number for vector ina.
Details
This is the like the "groupcolVars" (or rowsum), but only for vectors. No names are returned,
simply a vector, similar to "groupcolVars". Note that this command works only for vectors. Median
absolute deviation, mean, median, minium, maximum are some of the options offered.
Value
A vector with the variance, or standard deviation, or mean, or minimum, or maximum, or median,
or minimum-maximum of x for each distinct value of ina.
Sort - Sort a vector coresponding to another
231
Author(s)
Manos Papadakis and Michail Tsagris
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com> and Michail
Tsagris <mtsagris@yahoo.gr>.
See Also
groupcolVars, group.sum, colmeans, colVars, colMedians
Examples
x <- rgamma(100,1, 4)
ina <- sample(1:5, 100, TRUE)
group.var(x, ina)
#group.mean(x, ina) #run
#group.med(x, ina) #run
Sort - Sort a vector coresponding to another
Sort - Sort a vector coresponding to another
Description
Fast sorting a vector.
Usage
Sort(x,descending=FALSE,partial=NULL,stable=FALSE,na.last=NULL)
sort_cor_vectors(x, base, stable = FALSE, descending = FALSE)
Arguments
x
A numerical/character vector with data.
base
A numerical/character vector to help sorting the x.
descending
A boolean value (TRUE/FALSE) for sorting the vector in descending order. By
default sorts the vector in ascending.
partial
This argument has two usages. The first is an index number for sorting partial
the vector. The second is a vector with 2 values, start and end c(start,end). Gives
you a vector where the elements between start and end will be sorted only. Not
character vector.
stable
A boolean value (TRUE/FALSE) for choosing a stable sort algorithm. Stable
means that discriminates on the same elements. Not character vector.
na.last
Accept 4 values. TRUE, FALSE, NA, NULL.
TRUE/FALSE: for put NAs last or first.
NA: for remove NAs completely from vector.
NULL: by default. Leave it like that if there is no NA values.
232
Sort - Sort a vector coresponding to another
Details
This function uses the sorting algorithm from C++. The implementation is very fast and highly
optimised. Especially for large data.
Value
Sort: The sorted vector.
sort_cor_vectors: The first argument but sorted acording to the second.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
nth, colnth, rownth,sort_unique, Round
Examples
x <- rnorm(1000)
system.time( s1 <- Sort(x) )
system.time( s2 <- sort(x) )
all.equal(s1,s2) #true but not if many duplicates.
system.time( s1 <- Sort(x,partial=100) )
system.time( s2 <- sort(x,partial=100) )
all.equal(s1,s2) #true
system.time( s1 <- Sort(x,stable=TRUE) )
system.time( s2 <- sort(x) )
all.equal(s1,s2) #true
x <- as.character(x)
system.time( s1 <- Sort(x) )
system.time( s2 <- sort(x) )
all.equal(s1,s2) #true
y <- runif(1000)
b <- sort_cor_vectors(x,y)
x<-y<-y<-s1<-s2<-NULL
Sort and unique numbers
233
Sort and unique numbers
Sort and unique
Description
Sort and unique numbers.
Usage
sort_unique(x)
sort_unique.length(x)
Arguments
x
A numeric vector.
Details
The "sort_unique" function implements R’s "unique" function using C++’s function but also sort
the result. The "sort_unique.length" returns the length of the unique numbers.
Value
Returns the discrete values but sorted or their length (depending on the function you do).
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>
See Also
sort_mat, sort_cor_vectors
Examples
y <- rnorm(100)
a <- sort_unique(y)
b <- sort.int(unique(y))
all.equal(as.vector(a),as.vector(b))
x <- rpois(1000,10)
sort_unique.length(x)
length(sort_unique(x))
x<-a<-b<-NULL
234
Sorting of the columns-rows of a matrix
Sorting of the columns-rows of a matrix
Sorting of the columns-rows of a matrix
Description
Fast sorting of the columns-rows of a matrix.
Usage
sort_mat(x, by.row = FALSE, descending = FALSE, stable = FALSE,parallel=FALSE)
Arguments
x
A numerical matrix with data.
by.row
If you want to sort the rows of the matrix set this to TRUE.
descending
If you want the sorting in descending order, set this to TRUE.
stable
If you the stable version, so that the results are the same as R’s (in the case of
ties) set this to TRUE. If this is TRUE, the algorithm is a bit slower.
parallel
Do you want to do it in parallel in C++? TRUE or FALSE. Works with every
other argument.
Value
The matrix with its columns-rows (or rows) independently sorted.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
nth, colMaxs, colMins, colrange, sort_cor_vectors,sort_unique
Examples
x <- matrix( rnorm(100 * 500), ncol = 500 )
system.time( s1 <- sort_mat(x) )
system.time( s2 <- apply(x, 2, sort) )
all.equal(as.vector(s1), as.vector(s2))
x<-NULL
235
Source many R files
Source many R files
Source many R files
Description
Source many R/Rd files.
Usage
sourceR(path,local=FALSE,encode = "UTF-8",print.errors=FALSE)
sourceRd(path,print.errors=FALSE)
Arguments
path
An full path to the directory where R file are.
local
TRUE, FALSE or an environment, determining where the parsed expressions
are evaluated. FALSE (the default) corresponds to the user’s workspace (the
global environment) and TRUE to the environment from which source is called.
encode
Character vector. The encoding(s) to be assumed when file is a character string:
see file. A possible value is "unknown" when the encoding is guessed: see the
"Encodings" section.
print.errors
A boolean value (TRUE/FALSE) for printing the errors, if exists, for every file.
Details
Reads many R files and source them.
Value
Returns the files that had produced errors during source.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
read.directory, AddToNamespace
Examples
#
#
#
#
for example:
system.time(
for example:
system.time(
path="C:\some_file\R\" where is R files are
a<-sourceR(path) )
path="C:\some_file\man\" where is Rd files are
a<-sourceRd(path) )
236
Spatial median for Euclidean data
Spatial median for Euclidean data
Spatial median for Euclidean data
Description
Spatial median for Euclidean data.
Usage
spat.med(x, tol = 1e-09)
Arguments
x
A matrix with Euclidean data, continuous variables.
tol
A tolerance level to terminate the process. This is set to 1e-09 by default.
Details
The spatial median, using a fixed point iterative algorithm, for Euclidean data is calculated. It is a
robust location estimate.
Value
A vector with the spatial median.
Author(s)
Manos Papadakis and Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
References
Jyrki Mottonen, Klaus Nordhausen and Hannu Oja (2010). Asymptotic theory of the spatial median.
In Nonparametrics and Robustness in Modern Statistical Inference and Time Series Analysis: A
Festschrift in honor of Professor Jana Jureckova.
T. Karkkaminen and S. Ayramo (2005). On computation of spatial median for robust data mining.
Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications
to Industrial and Societal Problems, EUROGEN 2005, R. Schilling, W.Haase, J. Periaux, H. Baier,
G. Bugeda (Eds) FLM, Munich. http://users.jyu.fi/~samiayr/pdf/ayramo_eurogen05.pdf
See Also
colMedians
Spherical and hyperspherical median
237
Examples
spat.med( as.matrix( iris[, 1:4] ) )
colMeans( as.matrix(iris[, 1:4]) )
colMedians( as.matrix(iris[, 1:4]) )
Spherical and hyperspherical median
Fast calculation of the spherical and hyperspherical median
Description
It calculates, very fast, the (hyper-)spherical median of a sample.
Usage
mediandir(x)
Arguments
x
The data, a numeric matrix with unit vectors.
Details
The "mediandir" employes a fixed poit iterative algorithm stemming from the first derivative (Cabrera and Watson, 1990) to find the median direction as described in Fisher (1985) and Fisher, Lewis
and Embleton (1987).
Value
The median direction.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Fisher N. I. (1985). Spherical medians. Journal of the Royal Statistical Society. Series B, 47(2):
342-348.
Fisher N. I., Lewis T. and Embleton B. J. (1987). Statistical analysis of spherical data. Cambridge
university press.
Cabrera J. and Watson G. S. (1990). On a spherical median related distribution. Communications
in Statistics-Theory and Methods, 19(6): 1973-1986.
238
Standardisation
See Also
vmf.mle
Examples
m <- rnorm(3)
m <- m / sqrt( sum(m^2) )
x <- rvmf(100, m, 10)
mediandir(x)
x <- NULL
Standardisation
Standardisation
Description
Standardisation.
Usage
standardise(x, center = TRUE, scale = TRUE)
Arguments
x
A matrix with data. It has to be matrix, if it is data.frame for example the
function does not turn it into a matrix.
center
Should the data be centred as well? TRUE or FALSE.
scale
Should the columns have unit variance, yes (TRUE) or no (FALSE)?
Details
Similar to R’s built in functions "scale" there is the option for centering or scaling only or both
(default).
Value
A matrix with the standardised data.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
See Also
colVars, colmeans, colMads
239
Sub-matrix
Examples
x <- matrnorm( 100, 100 )
a1 <- scale(x)[1:100, ]
a2 <- standardise(x)
all.equal(as.vector(a1), as.vector(a2))
x <- NULL
Sub-matrix
Sub-matrix
Description
Sub-matrix.
Usage
submatrix(x,rowStart=1,rowEnd=1,colStart=1,colEnd=1)
Arguments
x
A Matrix, List, Dataframe or Vector.
rowStart
Start of the row.
rowEnd
End of the row.
colStart
Start of the col.
colEnd
End of the col.
Value
sub matrix like R’s, x[startrow:endrow,startcol:endcol]. Fast especially for big sub matrices.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
Match, mvbetas, correls, univglms, colsums, colVars
Examples
x <- matrix( rnorm(100 * 100), ncol = 100 )
submatrix(x,1,50,1,25) # x[1:50,1:25]
x<-NULL
240
Sum of all pairwise distances in a distance matrix
Sum of a matrix
Sum of a matrix
Description
Sum of a matrix.
Usage
matrix.sum(x)
Arguments
x
A matrix with data.
Value
The sum of the matrix "x".
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
rowMins, rowFalse, nth, colrange, colMedians, colVars, sort_mat, rowTrue
Examples
x <- matrix(runif(100*100),100,100)
f <- matrix.sum(x)
f==sum(x)
f<-NULL
Sum of all pairwise distances in a distance matrix
Sum of all pairwise distances in a distance matrix
Description
Sum of all pairwise distances in a distance matrix.
Sum of all pairwise distances in a distance matrix
241
Usage
total.dist(x, method = "euclidean", square = FALSE, p = 0)
total.dista(x, y, square = FALSE)
Arguments
x
A matrix with numbers.
y
A second matrix with data. The number of comlumns of this matrix must be the
same with the matrix x. The number of rows can be different.
method
This is either "euclidean", "manhattan", "canberra1", "canberra2", "minimum",
"maximum", "minkowski","bhattacharyya", "hellinger", "total_variation" or "kullback_leibler/jensen_shannon". The last two options are basically the same.
square
If you choose "euclidean" or "hellinger" as the method, then you can have the option to return the squared Euclidean distances by setting this argument to TRUE.
p
This is for the the Minkowski, the power of the metric.
Details
In order to do the total.dist one would have to calcualte the distance matrix and sum it. We do this
internally in C++ without creating the matrix. For the total.dista it is the same thing.
Value
A numerical value, the sum of the distances.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
Dist, dista
Examples
x <- matrix( rnorm(50 * 10), ncol = 10 )
total.dist(x)
y <- matrix( rnorm(40 * 10), ncol = 10)
total.dista(x, y)
total.dista(y, x)
x<-y<-NULL
242
Sums of a vector for each level of a grouping variable
Sums of a vector for each level of a grouping variable
Sums of a vector for each level of a grouping variable
Description
Sums of a vector for each level of a grouping variable.
Usage
group.sum(x, ina,ina.max = NULL,ina.min = NULL)
Arguments
x
A numerical vector whose sums are to be calculated for each value of "ina".
ina
A numerical vector or a factor variable. For evey distinct value of "ina" the sum
of "x" will be calculated. Note that negative values are not allowed as this can
cause R to run forever.
ina.min
Minimum INTEGER number for vector ina as vector or NULL.
ina.max
Maximum INTEGER number for vector ina as vector or NULL.
Details
This is the rowsum, but only for vectors. No names are returned, simply a matrix with one column,
just like rowsum. Note that this command works only for vectors.
Value
A matrix with one column, the sum of x for each distinct value of ina.
Author(s)
We found the C++ code (written by Francois Romain) in http://stackoverflow.com/questions/16975034/rcppequivalent-for-rowsum
Manos Papadakis then added it in Rfast.
R Documentation: Michail Tsagris <mtsagris@yahoo.gr>.
See Also
colmeans, colVars, Var, med
Examples
x <- rnorm(1000)
ina <- sample(1:5, 1000, replace = TRUE)
a1 <- group.sum(x, ina)
a2 <- rowsum(x, ina)
Table Creation - Frequency of each value
243
Table Creation - Frequency of each value
Table Creation - Frequency of each value
Description
Table Creation - Frequency of each value.
Usage
Table(x,y=NULL,names = TRUE,useNA = FALSE,rm.zeros = FALSE)
Table.sign(x,names = TRUE,useNA = FALSE)
Arguments
x
A vector with numeric/character data.
names
A logical value (TRUE/FALSE) for add names.
y
A vector with numeric/character data. Doesn’t work with "useNA".
rm.zeros
A logical value for removing zero columns/rows. Only for integer vectors for
now.
useNA
Table: Integer/logical value:
FALSE: not NA values in vector. TRUE: count NAs and add the value in the last
position of the returned vector. any other integer except 0,1: for just removing
NAs.
Table.sign: Logical value, TRUE, for count NAs. Otherwise FALSE.
Doesn’t work character data.
Details
Like R’s "table":
for giving one argument,"x": If "names" is FALSE then, if "useNA" is TRUE then the NAs will
be count, if is FALSE it means there are no NAs and for any other integer value the NAs will be
ignored.
for giving two arguments,"x","y": If "names" is FALSE then, creates the contigency table, otherwise
sets the col-row names with discrete values. If "rm.zeros" is FALSE then it won’t remove the zero
columns/rows from the result but it will work only for positive integers for now. For this if "names"
is TRUE then the col-row names will be the seq(min(),max()) for "x","y". In future updates it will
be changed.
for both algorithms: You can’t use "useNA" with "names" for now. It is much faster to get the result
without names (names = FALSE) but all the algorithms are more efficient than R’s.
Like R’s "table(sign())" but more efficient. Count the frequencies of positives, negatives, zeros and
NAs values. If argument "names" is FALSE then the returned vector doesn’t have names. Otherwise
"-1,0,+1,NA". If "useNA" is TRUE then the NAs will be count, otherwise not. You can use "useNA"
with "names".
244
Tests for the dispersion parameter in Poisson distribution
Value
Table:
for giving one argument,"x": if "names" is TRUE then return a vector with names the discrete values
of "x" and values there frequencies, otherwise only the frequencies
for giving two arguments,"x","y": if "names" is TRUE then return a contigency matrix with rownames the discrete values of "x", colnames the dicrete values of "y" and values the freuquencies of
the pairs, otherwise only the freuquencies of the pairs.
Table.sign: A vector with 4 values/frequencies: index 1: negatives index 2: zeros index 3: postives
if "names" is TRUE then the returned vector have names "-1,0,+1". if "useNA" is TRUE then 4th
value has the frequencies of NAs and the returned vector will have one more name, "-1,0,+1,NA",
if "names" is also TRUE.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colShuffle, colVars, colmeans, read.directory, is_integer, as_integer
Examples
x<-runif(10)
y1<-Table(x)
y2<-as.vector(table(x)) # Neads a lot of time.
all.equal(y1,y2)
y1<-Table(x,names=FALSE)
all.equal(y1,y2) # the name attribute of y1 is null
y1<-Table.sign(x)
y2<-table(sign(x))
all.equal(y1,y2)
x<-y1<-y2<-NULL
Tests for the dispersion parameter in Poisson distribution
Tests for the dispersion parameter in Poisson distribution
Description
Tests for the dispersion parameter in Poisson distribution.
Usage
poisdisp.test(y, alternative = "either", logged = FALSE)
pois.test(y, logged = FALSE)
Tests for the dispersion parameter in Poisson distribution
245
Arguments
y
A numerical vector with count data, 0, 1,...
alternative
Do you want to test specifically for either over or underspirsion ("either"), overdispersion ("over") or undersispersion ("under")?
logged
Set to TRUE if you want the logarithm of the p-value.
Value
A vector with two elements, the test statistic and the (logged) p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
References
Yang Zhao, James W. Hardin, and Cheryl L. Addy. (2009). A score test for overdispersion in
Poisson regression based on the generalized Poisson-2 model. Journal of statistical planning and
inference 139(4): 1514-1521.
Dimitris Karlis and Evdokia Xekalaki (2000). A Simulation Comparison of Several Procedures for
Testing the Poisson Assumption. Journal of the Royal Statistical Society. Series D (The Statistician), 49(3): 355-382.
Bohning, D., Dietz, E., Schaub, R., Schlattmann, P. and Lindsay, B. (1994) The distribution of the
likelihood ratio for mixtures of densities from the one-parameter exponential family. Annals of the
Institute of Statistical Mathematics, 46(): 373-388.
See Also
poisson.mle, negbin.mle, poisson.anova, poisson.anovas, poisson_only
Examples
y <- rnbinom(500, 10, 0.6)
poisdisp.test(y, "either")
poisdisp.test(y, "over")
pois.test(y)
y <- rpois(500, 10)
poisdisp.test(y, "either")
poisdisp.test(y, "over")
pois.test(y)
246
Topological sort of a DAG
Topological sort of a DAG
Topological sort of a DAG
Description
Topological sort of a DAG.
Usage
topological_sort(dag)
Arguments
dag
A square matrix representing a directed graph which contains 0s and 1s. If G[i,
j] = 1 it means there is an arrow from node i to node j. When there is no edge
between nodes i and j if G[i, j] = 0.
Details
The function is an R translation from an old matlab code.
Value
A vector with numbers indicating the sorting. If the dag is not a Directed acyclic Graph, NA will
be returned.
Author(s)
Michail Tsagris and Manos Papadakis
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>
References
Chickering, D.M. (1995). A transformational characterization of equivalent Bayesian network
structures. Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence, Montreal,
Canada, 87-98.
See Also
floyd, pc.skel
247
Transpose of a matrix
Examples
G <- matrix(0, 5, 5)
G[2, 1] <- 1
G[3, 1] <- 1
G[4, 2] <- 1
G[5, 4] <- 1
topological_sort(G)
G[2, 4] <- 1
topological_sort(G)
Transpose of a matrix Transpose of a matrix
Description
Transpose of a matrix.
Usage
transpose(x)
Arguments
x
A numerical square matrix with data.
Value
The transposed matrix.
Author(s)
Manos Papadakis
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
References
Gilbert Strang (2006). Linear Algebra and its Applications (4th edition).
See Also
nth, colMaxs, colMins, colrange
Examples
x <- matrix( rnorm(500 * 500), ncol = 500, nrow=500 )
system.time( transpose(x) )
system.time( t(x) )
x<-NULL
248
Two sample exponential empirical likelihood test
Two sample exponential empirical likelihood test
Two sample exponential empirical likelihood test
Description
Two sample exponential empirical likelihood test.
Usage
eel.test2(x, y, tol = 1e-09, logged = FALSE)
Arguments
x
A numerical vector.
y
Another numerical vector.
tol
The tolerance value to stop the iterations of the Newton-Raphson.
logged
Should the logarithm of the p-value be returned? TRUE or FALSE.
Details
Exponential empirical likelihood is a non parametric method. In this case we use it as the non
parametric alternative to the t-test. Newton-Raphson is used to maximise the log-likelihood ratio
test statistic. In the case of no solution, NULL is returned.
Value
iters
The number of iterations required by the Newton-Raphson algorithm. If no
covnergence occured this is NULL.
info
A vector with three elements, the value of the λ, the likelihood ratio test statistic
and the relevant p-value. If no convergence occured, the value of the λ before is
becomes NA, the value of test statistic is 105 and the p-value is 0. No convergence can be interpreted as rejection of the hypothesis test.
p1
The estimated probabilities, one for each observation for the first sample. If no
covnergence occured this is NULL.
p2
The estimated probabilities, one for each observation for the second sample. If
no covnergence occured this is NULL.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Uniformity test for circular data
249
References
Owen A. B. (2001). Empirical likelihood. Chapman and Hall/CRC Press.
See Also
ftests, ttests,, ttest
Examples
x <- rnorm(100)
y <- rnorm(200)
system.time( eel.test2(x, y) )
x <- rnorm(100)
system.time( eel.test2(x, y) )
x <- rnorm(50)
y <- rexp(100)
system.time( eel.test2(x, y) )
Uniformity test for circular data
Uniformity tests for circular data
Description
Hypothesis tests of uniformity for circular data.
Usage
kuiper(u)
watson(u)
Arguments
u
A numeric vector containing the circular data which are expressed in radians.
Details
These tests are used to test the hypothesis that the data come from a circular uniform distribution.
Value
A vector with two elements, the value of the test statistic and its associated p-value.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
250
Variance of a vector
References
Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, pg. 153-55
(Kuiper’s test) & 156-157 (Watson’s test).
See Also
vmf.mle, rvonmises
Examples
x <- rvonmises(n = 50, m = 2, k = 10)
kuiper(x)
watson(x)
x <- runif(50, 0, 2 * pi)
kuiper(x)
watson(x)
Variance of a vector
Variance (and standard deviation) of a vector
Description
Variance (and standard deviation) of a vector.
Usage
Var(x, std = FALSE,na.rm = FALSE)
Arguments
x
A vector with data.
std
If you want the standard deviation set this to TRUE, otherwise leave it FALSE.
na.rm
TRUE or FAlSE for remove NAs if exists.
Details
This is a faster calculaiton of the usual variance of a matrix.
Value
The variance of the vector.
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr> and Manos Papadakis
<papadakm95@gmail.com>.
Vector allocation in a symmetric matrix
251
See Also
colVars, cova
Examples
x <- rnorm(1000)
system.time( for (i in 1:100) Var(x) )
#system.time( for (i in 1:100) var(x) )
x<-NULL
Vector allocation in a symmetric matrix
Vector allocation in a symmetric matrix
Description
Vector allocation in a symmetric matrix.
Usage
squareform(x)
Arguments
x
An numverical vector whose size must be the one that matches the dimensions
of the final matrix. See examples.
Details
The functions is written in C++ in order to be as fast as possible.
Value
A symmetric matrix. The vector is allocated in the upper and in the lower part of the matrix. The
diagonal is filled with zeros.
Author(s)
R implementation and documentation: Manos Papadakis <papadakm95@gmail.com>.
See Also
colShuffle, colVars, colmeans
252
Weibull regression model
Examples
x <- rnorm(1)
squareform(x)
x <- rnorm(3)
squareform(x)
x <- rnorm(4)
squareform(x)
## OK
## OK
## not OK
Weibull regression model
Weibull regression model
Description
Weibull regression model.
Usage
weib.reg(y, x, tol = 1e-07, maxiters = 100)
Arguments
y
The dependent variable; a numerical vector with strictly positive data, i.e. greater
than zero.
x
A matrix with the data, where the rows denote the samples (and the two groups)
and the columns are the variables. This can be a matrix or a data.frame (with
factors).
tol
The tolerance value to terminate the Newton-Raphson algorithm.
maxiters
The max number of iterations that can take place in each regression.
Details
The function is written in C++ and this is why it is very fast. No standard errors are returned as they
are not corectly estimated. We focused on speed.
Value
When full is FALSE a list including:
iters
The iterations required by the Newton-Raphson.
loglik
The log-likelihood of the model.
shape
The shape parameter of the Weibull regression.
be
The regression coefficients.
Yule’s Y (coefficient of colligation)
253
Author(s)
Stefanos Fafalios
R implementation and documentation: Stefanos Fafalios <stefanosfafalios@gmail.com>.
References
McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition,
1989.
See Also
poisson_only, logistic_only, univglms, regression
Examples
x <- matrix(rnorm(100 * 2), ncol = 2)
y <- rexp(100, 1)
weib.reg(y, x)
x <- NULL
Yule’s Y (coefficient of colligation)
Yule’s Y (coefficient of colligation)
Description
Yule’s Y (coefficient of colligation).
Usage
yule(x)
Arguments
x
A 2 x 2 matrix or a vector with 4 elements. In the case of the vector make sure
it corresponds to the correct table.
Details
Yule’s coefficient of colligation is calculated.
Value
Yule’s Y is returned.
254
Yule’s Y (coefficient of colligation)
Author(s)
Michail Tsagris
R implementation and documentation: Michail Tsagris <mtsagris@yahoo.gr>
References
Yule G. Udny (1912). On the Methods of Measuring Association Between Two Attributes. Journal
of the Royal Statistical Society, 75(6):579-652.
See Also
col.yule, odds.ratio
Examples
x <- rpois(4, 30) + 2
yule(x)
yule( matrix(x, ncol = 2) )
Index
∗Topic 2 sample proportions tests
Many 2 sample proportions tests,
112
∗Topic 2 variances test
Many 2 sample tests, 113
∗Topic AR(1) model
Estimation of an AR(1) model, 72
∗Topic All possibe combinations
All k possible combinations from n
elements, 7
∗Topic Analysis of covariance
Analysis of covariance, 8
Many ANCOVAs, 116
∗Topic Analysis of variance
Analysis of variance with a count
variable, 9
∗Topic Angular central Gaussian
∗Topic Canberra distance
Distance matrix, 66
∗Topic Cauchy
MLE of continuous univariate
distributions defined on the
real line, 171
∗Topic Checking Alias
Check Namespace and Rd files, 21
∗Topic Checking Examples
Check Namespace and Rd files, 21
∗Topic Checking Rd
Check Namespace and Rd files, 21
∗Topic Checking R
Check Namespace and Rd files, 21
∗Topic Checking for TRUE,FALSE
Check Namespace and Rd files, 21
∗Topic Cholesky decomposition
Cholesky decomposition of a
square matrix, 24
∗Topic Circular data
Column-wise uniformity Watson
test for circular data, 50
Uniformity test for circular data,
249
∗Topic Circular regression
Circular or angular regression, 25
Many simple circular or angular
regressions, 141
∗Topic Circular-linear correlation
Circular-linear correlation, 27
∗Topic Cochran’s Q test
Many non parametric multi-sample
tests, 128
∗Topic Column means
Column and row-wise means of a
matrix, 30
∗Topic Column sums
Column and row-wise sums of a
matrix, 38
distribution
Angular central Gaussian random
values simulation, 10
∗Topic Area aunder the curve
Many (and one) area aunder the
curve values, 111
∗Topic BIC
BIC (using partial correlation)
forward regression, 14
BIC forward regression with
generalised linear models, 15
∗Topic Beta distribution
MLE of distributions defined in
the (0, 1) interval, 174
∗Topic Beta function
Natural logarithm of the beta
function, 192
∗Topic Binary search Algorithm
Binary search algorithm, 16
∗Topic Bradley-Terry model
Fitted probabilities of the
Terry-Bradley model, 80
255
256
INDEX
∗Topic Column-Row wise checking
Check if any column or row is fill
with zeros, 19
∗Topic Column-wise Any
Column and row-wise Any/All, 29
∗Topic Column-wise Shuffle
Column and row-wise Shuffle, 37
∗Topic Column-wise median absolute
deviations
Column and rows-wise mean
absolute deviations, 41
∗Topic Column-wise medians
Column and row-wise medians, 31
∗Topic Column-wise minimum
Column-wise minimum and maximum, 46
∗Topic Column-wise nth
Column and row-wise nth smallest
value of a matrix/vector, 32
∗Topic Column-wise ranges
Column and row-wise range of
values of a matrix, 35
∗Topic Column-wise tabulate
Column and row-wise tabulate, 39
∗Topic Column-wise true
Column-wise true/false value, 49
∗Topic Column-wise variances
Column and row-wise variances and
standard deviations, 40
∗Topic Column-wise
Column-wise MLE of some
univariate distributions, 47
∗Topic Combinatorics
All k possible combinations from n
elements, 7
∗Topic Continuous distributions
MLE of continuous univariate
distributions defined on the
positive line, 169
MLE of continuous univariate
distributions defined on the
real line, 171
∗Topic Correlations
Correlation between pairs of
variables, 53
Correlations, 55
∗Topic Covariance matrix
Covariance and correlation matrix,
56
∗Topic Create - Fill
Diagonal Matrix, 63
∗Topic DAG
Topological sort of a DAG, 246
∗Topic Dataframe to Matrix
data.frame.to_matrix, 60
∗Topic Design Matrix
Design Matrix, 62
∗Topic Determinant
Check if any column or row is fill
with zeros, 19
∗Topic Diagonal Matrix
Diagonal Matrix, 63
∗Topic Differences
Column-wise differences, 43
∗Topic Directional k-NN algorithm
k-NN algorithm using the arc
cosinus distance, 103
∗Topic Dirichlet distribution
Fitting a Dirichlet distribution
via Newton-Rapshon, 81
∗Topic Discrimination
Prediction with some naive Bayes
classifiers, 204
∗Topic Distance correlation
Distance correlation, 65
∗Topic Distance covariance
Distance variance and covariance,
67
∗Topic Distance matrix
Distance matrix, 66
∗Topic Distance variance
Distance variance and covariance,
67
∗Topic Distances
Distance between vectors and a
matrix, 64
Sum of all pairwise distances in a
distance matrix, 240
∗Topic Divide and Qonquer
Binary search algorithm, 16
Find element, 78
∗Topic Eigenvalues
Eigenvalues and eigenvectors in
high dimensional principal
component analysis, 68
∗Topic Energy distances
Energy distance between matrices,
257
INDEX
70
∗Topic Equality check
Equality of objects, 71
∗Topic Euclidean distance
Distance matrix, 66
∗Topic Exponential regressions
Many exponential regressions, 117
∗Topic Export functions
Insert new function names in the
NAMESPACE file, 98
Source many R files, 235
∗Topic Extract columns/rows
Get specific columns/rows fo a
matrix, 89
∗Topic F-tests
Many F-tests with really huge
matrices, 118
Many multi-sample tests, 125
∗Topic F-test
Multi-sample tests for vectors, 183
∗Topic Factor variables
Index of the columns of a
data.frame which are factor
variables, 97
∗Topic Factorials
Binomial coefficient and its
logarithm, 17
∗Topic Find Value
Find the given value in a hash
table, 79
∗Topic Find element
Find element, 78
∗Topic Floyd-Warshall algorithm
Floyd-Warshall algorithm, 82
∗Topic Forward regression
BIC (using partial correlation)
forward regression, 14
BIC forward regression with
generalised linear models, 15
Correlation based forward
regression, 52
Forward selection with generalised
linear regression models, 84
∗Topic GLMS
Many score based GLM regressions,
136
∗Topic GLMs
Quasi binomial regression for
proportions, 205
Quasi Poisson regression for
count data, 207
Significance testing for the
coefficients of Quasi
binomial or the quasi Poisson
regression, 221
∗Topic G^2 test of conditional
independence
G-square test of conditional
indepdence, 85
∗Topic G^2 test of independence
Matrix with G-square tests of
indepedence, 159
∗Topic G^2 tests of independence
Many G-square tests of
indepedence, 119
∗Topic Gini coefficient
Many Gini coefficients, 121
∗Topic Goodness of fit test
Hypothesis test for von
Mises-Fisher distribution
over Kent distribution, 95
∗Topic Grouped sums
Sums of a vector for each level of
a grouping variable, 242
∗Topic Gumbel distribution
MLE of continuous univariate
distributions defined on the
real line, 171
∗Topic Hash Function
Find the given value in a hash
table, 79
Hash - Pair function, 90
∗Topic Hash tables
Hash object to a list object, 91
∗Topic Hellinger distance
Distance matrix, 66
∗Topic High dimensional data
High dimensional MCD based
detection of outliers, 92
∗Topic Hypothesis testing
Many one sample tests, 131
One sample empirical and
exponential empirical
likelihood test, 197
Two sample exponential empirical
likelihood test, 248
258
∗Topic Hypothesis test
Exponential empirical likelihood
for a one sample mean vector
hypothesis testing, 74
∗Topic Inverse matrix
Inverse of a symmetric positive
definite matrix, 99
∗Topic Inverted Dirichlet distribution
MLE of the inverted Dirichlet
distribution, 177
∗Topic James test
Multi-sample tests for vectors, 183
∗Topic Kent distribution
Hypothesis test for von
Mises-Fisher distribution
over Kent distribution, 95
∗Topic Laplace distribution
MLE of continuous univariate
distributions defined on the
real line, 171
∗Topic Linear mixed models
Column and row wise coefficients
of variation, 28
Many random intercepts LMMs for
balanced data with a single
identical covariate., 133
Random intercepts linear mixed
models, 209
∗Topic Linear models
Linear models for large scale
data, 104
∗Topic Linear time
Find element, 78
∗Topic Log matrix
Natural Logarithm each element of
a matrix, 191
∗Topic Logarithm of gamma function
Natural logarithm of the gamma
function and its derivatives,
193
∗Topic Logistic distribution
MLE of continuous univariate
distributions defined on the
real line, 171
∗Topic Logistic regressions
Many univariate simple binary
logistic regressions, 151
∗Topic Logistic regression
INDEX
Logistic and Poisson regression
models, 105
Logistic or Poisson regression
with a single categorical
predictor, 107
∗Topic Lower and Upper triangular
of a matrix
Lower and Upper triangular of a
matrix, 108
∗Topic MCD estimation
High dimensional MCD based
detection of outliers, 92
∗Topic Mahalanobis distance
Mahalanobis distance, 110
∗Topic Manhattan distance
Distance matrix, 66
∗Topic Many betas in regression
Many multivariate simple linear
regressions coefficients, 127
Many simple linear regressions
coefficients, 145
∗Topic Match Function
Match, 157
∗Topic Matrices
Number of equal columns between
two matrices, 195
∗Topic McNemar’s test
Many 2 sample tests, 113
∗Topic Median direction
Spherical and hyperspherical
median, 237
∗Topic Multinomial distribution
MLE for multivariate discrete
data, 166
Multinomial regression, 185
∗Topic Multivariate analysis of
variance
James multivariate version of the
t-test, 100
∗Topic Multivariate data
Multivariate kurtosis, 186
∗Topic Multivariate hypothesis testing
Exponential empirical likelihood
hypothesis testing for two
mean vectors, 75
∗Topic Multivariate normal
distribution
Density of the multivariate
INDEX
normal and t distributions, 61
MLE of the multivariate normal
distribution, 178
∗Topic Namespace file
Check Namespace and Rd files, 21
Insert new function names in the
NAMESPACE file, 98
Source many R files, 235
∗Topic Newton-Raphson
Fitting a Dirichlet distribution
via Newton-Rapshon, 81
MLE of distributions defined in
the (0, 1) interval, 174
∗Topic Norm of a matrix
Norm of a matrix, 194
∗Topic Odds ratios
Many odds ratio tests, 129
∗Topic Odds ratio
Odds ratio and relative risk, 196
∗Topic One sample t-test
One sample t-test for a vector, 198
∗Topic Orderings
Column and row-wise Order - Sort
Indices, 33
∗Topic Ordinal model
MLE of the ordinal model without
covariates, 179
∗Topic PC algorithm
Skeleton of the PC algorithm, 227
∗Topic Pair Function
Hash - Pair function, 90
∗Topic Pairs of vectors
Column-row wise minima and maxima
of two matrices, 42
Minima and maxima of two
vectors/matrices, 163
∗Topic Pareto
MLE of continuous univariate
distributions defined on the
positive line, 169
∗Topic Pearson correlation
Correlation based forward
regression, 52
∗Topic Permutation Function
Permutation, 202
∗Topic Poisson distribution
Analysis of variance with a count
variable, 9
259
Many analysis of variance tests
with a discrete variable, 114
Many tests for the dispersion
parameter in Poisson
distribution, 147
MLE of count data (univariate
discrete distributions), 172
Prediction with some naive Bayes
classifiers, 204
Tests for the dispersion parameter
in Poisson distribution, 244
∗Topic Poisson regressions
Many univariate simple poisson
regressions, 154
Many univariate simple quasi
poisson regressions, 155
∗Topic Poisson regression
Logistic or Poisson regression
with a single categorical
predictor, 107
∗Topic Poisson
Forward selection with generalised
linear regression models, 84
∗Topic Products
Column and row-wise products, 34
∗Topic Quasi Poisson regression
Quasi Poisson regression for
count data, 207
∗Topic Quasi regression
Quasi binomial regression for
proportions, 205
Significance testing for the
coefficients of Quasi
binomial or the quasi Poisson
regression, 221
∗Topic Random values simulation
Random values simulation from a
von Mises distribution, 210
Simulation of random values from a
von Mises-Fisher distribution,
225
∗Topic Read Examples
Reading the files of a directory,
212
∗Topic Read directory
Reading the files of a directory,
212
∗Topic Repeated measures
260
INDEX
Many regression based tests for
single sample repeated
measures, 134
Repeated measures anova, 214
∗Topic Replicate in columns/rows
Replicate columns/rows, 215
∗Topic Replicate in columns
Sum of a matrix, 240
∗Topic Round vector/matrix
Round each element of a
matrix/vector, 216
∗Topic Row - Wise matrix/vector
count the frequency of a
value
Row - Wise matrix/vector count the
frequency of a value, 217
∗Topic Row sums
Column and row-wise sums of a
matrix, 38
∗Topic Row-wise Any
Column and row-wise Any/All, 29
∗Topic Row-wise Shuffle
Column and row-wise Shuffle, 37
∗Topic Row-wise false
Row-wise true value, 219
∗Topic Row-wise medians
Column and row-wise medians, 31
∗Topic Row-wise minimum
Row-wise minimum and maximum, 218
∗Topic Row-wise nth
Column and row-wise nth smallest
value of a matrix/vector, 32
∗Topic Row-wise tabulate
Column and row-wise tabulate, 39
∗Topic Row-wise true-false
Row-wise true value, 219
∗Topic Row-wise true
Row-wise true value, 219
∗Topic Shapiro-Francia
Many Shapiro-Francia normality
tests, 139
∗Topic Significance testing
Significance testing for the
coefficients of Quasi
binomial or the quasi Poisson
regression, 221
∗Topic Simple linear regressions
Many univariate simple linear
regressions, 152
∗Topic Skewness coefficient
Column-wise kurtosis and skewness
coefficients, 44
∗Topic Skewness
Hypothesis testing betseen two
skewness or kurtosis
coefficients, 96
Skewness and kurtosis
coefficients, 229
∗Topic Sort function
Sort and unique numbers, 233
∗Topic Sorting 2 vectors
Sort - Sort a vector coresponding
to another, 231
∗Topic Sorting
Sort - Sort a vector coresponding
to another, 231
Sorting of the columns-rows of a
matrix, 234
∗Topic Stable Sorting
Sort - Sort a vector coresponding
to another, 231
∗Topic Standardisation
Standardisation, 238
∗Topic Sub-matrix
Sub-matrix, 239
∗Topic Sum
Operations between two matrices
or matrix and vector, 200
∗Topic Supervised classification
k-NN algorithm using the arc
cosinus distance, 103
∗Topic Symmetric matrix
Check whether a square matrix is
symmetric, 23
∗Topic Table Creation
Table Creation - Frequency of each
value, 243
∗Topic Time series
Estimation of an AR(1) model, 72
∗Topic Tobit model
MLE of the tobit model, 180
∗Topic Topological sort
Topological sort of a DAG, 246
∗Topic Transpose
Transpose of a matrix, 247
∗Topic Two-way ANOVA
261
INDEX
Many two-way ANOVAs, 148
∗Topic Unequality of the covariance
matrices
James multivariate version of the
t-test, 100
∗Topic Univariate normality test
Many Shapiro-Francia normality
tests, 139
∗Topic Variance components
Moment and maximum likelihood
estimation of variance
components, 181
∗Topic Variance
Some summary statistics of a
vector for each level of a
grouping variable, 230
Variance of a vector, 250
∗Topic Weibull regressions
Many score based regression
models, 138
∗Topic Weibull
MLE of continuous univariate
distributions defined on the
positive line, 169
∗Topic Wigner semicircle distribution
MLE of continuous univariate
distributions defined on the
real line, 171
∗Topic Zero range
Search for variables with zero
range in a matrix, 220
∗Topic analysis of variance
Logistic or Poisson regression
with a single categorical
predictor, 107
Many analysis of variance tests
with a discrete variable, 114
Many F-tests with really huge
matrices, 118
Many multi-sample tests, 125
Many non parametric multi-sample
tests, 128
Multi-sample tests for vectors, 183
∗Topic balanced design
Column and row wise coefficients
of variation, 28
Many random intercepts LMMs for
balanced data with a single
identical covariate., 133
Random intercepts linear mixed
models, 209
∗Topic beta prime
MLE of continuous univariate
distributions defined on the
positive line, 169
∗Topic beta regressions
Many score based regression
models, 138
∗Topic bias corrected
Distance correlation, 65
∗Topic binary data
Forward selection with generalised
linear regression models, 84
∗Topic binomial distribution
MLE of count data (univariate
discrete distributions), 172
∗Topic bivariate angular Gaussian
MLE of some circular
distributions, 176
∗Topic blocking ANOVA
Many multi-sample tests, 125
Multi-sample tests for vectors, 183
∗Topic categorical variables
Many univariate simple linear
regressions, 152
∗Topic censored observations
MLE of the tobit model, 180
∗Topic central angular Gaussian
distribution
MLE of (hyper-)spherical
distributions, 167
∗Topic circular data
MLE of some circular
distributions, 176
∗Topic column-wise false
Column-wise true/false value, 49
∗Topic column-wise maximum
Column-wise minimum and maximum, 46
∗Topic column-wise
minimum-maximum
Column-wise minimum and maximum, 46
∗Topic column-wise true-false
Column-wise true/false value, 49
∗Topic combinatorics
Binomial coefficient and its
logarithm, 17
262
∗Topic conditional MLE
Estimation of an AR(1) model, 72
∗Topic continuous distributions
Column-wise MLE of some
univariate distributions, 47
∗Topic cross-validation
Cross-Validation for the k-NN
algorithm, 58
∗Topic data check
Search for variables with zero
range in a matrix, 220
∗Topic density values
Density of the multivariate
normal and t distributions, 61
∗Topic dependent binary data
Multi-sample tests for vectors, 183
∗Topic derivatives
Natural logarithm of the gamma
function and its derivatives,
193
∗Topic digamma function
Natural logarithm of the gamma
function and its derivatives,
193
∗Topic directed graph
Floyd-Warshall algorithm, 82
∗Topic directional data
Angular central Gaussian random
values simulation, 10
MLE of (hyper-)spherical
distributions, 167
∗Topic discrete distributions
Column-wise MLE of some
univariate distributions, 47
∗Topic dispersion parameter
Many tests for the dispersion
parameter in Poisson
distribution, 147
Tests for the dispersion parameter
in Poisson distribution, 244
∗Topic equality of variances
Many multi-sample tests, 125
Multi-sample tests for vectors, 183
∗Topic excessive zeros
MLE of count data (univariate
discrete distributions), 172
∗Topic exponential regressions
Many score based regression
INDEX
models, 138
∗Topic fitted probabilities
Fitted probabilities of the
Terry-Bradley model, 80
∗Topic folded normal
MLE of continuous univariate
distributions defined on the
positive line, 169
∗Topic fractional response
Quasi binomial regression for
proportions, 205
Significance testing for the
coefficients of Quasi
binomial or the quasi Poisson
regression, 221
∗Topic gamma distribution
MLE of continuous univariate
distributions defined on the
positive line, 169
∗Topic gamma regressions
Many score based regression
models, 138
∗Topic generalised linear models
Logistic and Poisson regression
models, 105
Many univariate simple binary
logistic regressions, 151
Many univariate simple poisson
regressions, 154
Many univariate simple quasi
poisson regressions, 155
∗Topic geometric distribution
Analysis of variance with a count
variable, 9
Many analysis of variance tests
with a discrete variable, 114
MLE of count data (univariate
discrete distributions), 172
∗Topic grouppings
Some summary statistics of a
vector for each level of a
grouping variable, 230
∗Topic half normal
MLE of continuous univariate
distributions defined on the
positive line, 169
∗Topic harmonic means
Column and row-wise means of a
263
INDEX
matrix, 30
∗Topic high dimensional data
Eigenvalues and eigenvectors in
high dimensional principal
component analysis, 68
∗Topic huge datasets
Many F-tests with really huge
matrices, 118
∗Topic hypersecant distribution for
proportions
MLE of distributions defined in
the (0, 1) interval, 174
∗Topic hypothesis testing
Column-wise uniformity Watson
test for circular data, 50
Hypothesis testing betseen two
skewness or kurtosis
coefficients, 96
Uniformity test for circular data,
249
∗Topic inflated beta distribution
MLE of distributions defined in
the (0, 1) interval, 174
∗Topic interaction
Many two-way ANOVAs, 148
∗Topic is_integer Creation
Check if values are integers and
convert to integer, 20
∗Topic k-NN algorithm
Cross-Validation for the k-NN
algorithm, 58
k nearest neighbours algorithm
(k-NN), 101
∗Topic kurtosis coefficient
Column-wise kurtosis and skewness
coefficients, 44
∗Topic kurtosis
Hypothesis testing betseen two
skewness or kurtosis
coefficients, 96
Multivariate kurtosis, 186
Skewness and kurtosis
coefficients, 229
∗Topic large scale data
Linear models for large scale
data, 104
∗Topic left censoring
MLE of the tobit model, 180
∗Topic list
Hash object to a list object, 91
∗Topic logarithm
Natural logarithm of the beta
function, 192
∗Topic logistic normal distribution
MLE of distributions defined in
the (0, 1) interval, 174
∗Topic matrix
Column and row-wise Order - Sort
Indices, 33
Column and row-wise products, 34
Column-wise differences, 43
Transpose of a matrix, 247
∗Topic maximum frequency
minimum and maximum frequencies,
165
∗Topic maximum likelihood
estimation
Column and row wise coefficients
of variation, 28
Fitting a Dirichlet distribution
via Newton-Rapshon, 81
Many random intercepts LMMs for
balanced data with a single
identical covariate., 133
MLE of (hyper-)spherical
distributions, 167
MLE of distributions defined in
the (0, 1) interval, 174
Moment and maximum likelihood
estimation of variance
components, 181
Random intercepts linear mixed
models, 209
∗Topic maximum
Column-row wise minima and maxima
of two matrices, 42
Minima and maxima of two
vectors/matrices, 163
minimum and maximum, 164
∗Topic mean vector
Exponential empirical likelihood
for a one sample mean vector
hypothesis testing, 74
∗Topic minimum frequency
minimum and maximum frequencies,
165
264
INDEX
∗Topic minimum
Column-row wise minima and maxima
of two matrices, 42
Minima and maxima of two
vectors/matrices, 163
minimum and maximum, 164
∗Topic moments estimation
Moment and maximum likelihood
estimation of variance
components, 181
∗Topic multinomial distribution
Prediction with some naive Bayes
classifiers, 204
∗Topic multinomial regressions
Many score based GLM regressions,
136
∗Topic multivariate Laplace
distribution
Multivariate Laplace random
values simulation, 187
∗Topic multivariate discrete data
MLE for multivariate discrete
data, 166
∗Topic multivariate normal
distribution
Multivariate normal and t random
values simulation, 188
∗Topic multivariate t distribution
Density of the multivariate
normal and t distributions, 61
∗Topic naive Bayes
Prediction with some naive Bayes
classifiers, 204
∗Topic negative binomial
MLE of count data (univariate
discrete distributions), 172
∗Topic non parametric statistics
Many non parametric multi-sample
tests, 128
∗Topic non parametric test
Exponential empirical likelihood
hypothesis testing for two
mean vectors, 75
One sample empirical and
exponential empirical
likelihood test, 197
Two sample exponential empirical
likelihood test, 248
∗Topic normal distribution
Prediction with some naive Bayes
classifiers, 204
∗Topic nth elements
Column and row-wise nth smallest
value of a matrix/vector, 32
Median of a vector, 162
∗Topic one sample
Many one sample tests, 131
One sample empirical and
exponential empirical
likelihood test, 197
∗Topic operations
Operations between two matrices
or matrix and vector, 200
∗Topic outliers
High dimensional MCD based
detection of outliers, 92
∗Topic partial correlation
BIC (using partial correlation)
forward regression, 14
Correlation based forward
regression, 52
∗Topic percentages
Hypothesis test for two means of
percentages, 94
Many hypothesis tests for two
means of percentages, 122
∗Topic poisson regression
Logistic and Poisson regression
models, 105
∗Topic positive definite
Inverse of a symmetric positive
definite matrix, 99
∗Topic positive multivariate data
MLE of the inverted Dirichlet
distribution, 177
∗Topic projected normal distribution
MLE of (hyper-)spherical
distributions, 167
∗Topic projected normal
Circular or angular regression, 25
Many simple circular or angular
regressions, 141
∗Topic proportion test
Many one sample tests, 131
∗Topic proportional odds
MLE of the ordinal model without
INDEX
covariates, 179
∗Topic proportions
Forward selection with generalised
linear regression models, 84
MLE of distributions defined in
the (0, 1) interval, 174
∗Topic random values simulation
Angular central Gaussian random
values simulation, 10
Multivariate Laplace random
values simulation, 187
Multivariate normal and t random
values simulation, 188
∗Topic regression
Many regression based tests for
single sample repeated
measures, 134
Multinomial regression, 185
Repeated measures anova, 214
∗Topic robust statistics
Spatial median for Euclidean data,
236
∗Topic row means
Column and row-wise means of a
matrix, 30
∗Topic row-wise maximum
Row-wise minimum and maximum, 218
∗Topic row-wise variances
Column and row-wise variances and
standard deviations, 40
∗Topic score based tests
Many score based GLM regressions,
136
Many score based regression
models, 138
∗Topic shortest paths
Floyd-Warshall algorithm, 82
∗Topic single categorical predictor
Logistic or Poisson regression
with a single categorical
predictor, 107
∗Topic sorting
Median of a vector, 162
∗Topic spatial median
Spatial median for Euclidean data,
236
∗Topic spherical data
MLE of (hyper-)spherical
265
distributions, 167
∗Topic summary statistics
Many regression based tests for
single sample repeated
measures, 134
Repeated measures anova, 214
∗Topic symmetric matrix
Inverse of a symmetric positive
definite matrix, 99
Vector allocation in a symmetric
matrix, 251
∗Topic t distribution
MLE of continuous univariate
distributions defined on the
real line, 171
∗Topic t-tests
Many 2 sample tests, 113
Many hypothesis tests for two
means of percentages, 122
Matrix with all pairs of t-tests,
158
∗Topic t-test
Hypothesis test for two means of
percentages, 94
Many one sample tests, 131
∗Topic total sum
Energy distance between matrices,
70
Sum of all pairwise distances in a
distance matrix, 240
∗Topic trigamma function
Natural logarithm of the gamma
function and its derivatives,
193
∗Topic two samples
Two sample exponential empirical
likelihood test, 248
∗Topic uniformity tests
Column-wise uniformity Watson
test for circular data, 50
∗Topic uniformity test
Uniformity test for circular data,
249
∗Topic unique numbers
Sort and unique numbers, 233
∗Topic univariate approach
Many regression based tests for
single sample repeated
266
measures, 134
Repeated measures anova, 214
∗Topic variable selection
Forward selection with generalised
linear regression models, 84
∗Topic variance test
Many one sample tests, 131
∗Topic variances of many samples
Column and row-wise variances and
standard deviations, 40
∗Topic von Mises distribution
MLE of some circular
distributions, 176
∗Topic von Mises-Fisher distribution
Hypothesis test for von
Mises-Fisher distribution
over Kent distribution, 95
MLE of (hyper-)spherical
distributions, 167
Random values simulation from a
von Mises distribution, 210
Simulation of random values from a
von Mises-Fisher distribution,
225
∗Topic wrapped Cauchy distribution
MLE of some circular
distributions, 176
∗Topic zero inflated Poisson
MLE of count data (univariate
discrete distributions), 172
∗Topic zero truncated Poisson
MLE of count data (univariate
discrete distributions), 172
.lm.fit, 105
AddToNamespace (Insert new function
names in the NAMESPACE file),
98
acg.mle, 11, 26, 142
acg.mle (MLE of (hyper-)spherical
distributions), 167
AddToNamespace, 23, 213, 235
All k possible combinations from n
elements, 7
all_equals (Equality of objects), 71
allbetas, 54, 55, 87, 105, 127, 143, 145,
151–154, 156, 157
INDEX
allbetas (Many simple linear
regressions coefficients), 145
allttests (Matrix with all pairs of
t-tests), 158
Analysis of covariance, 8
Analysis of variance with a count
variable, 9
ancova1 (Analysis of covariance), 8
ancovas, 9, 149
ancovas (Many ANCOVAs), 116
Angular central Gaussian random
values simulation, 10
anova, 10, 81, 108, 115
ANOVA for two quasi Poisson regression
models, 11
anova1, 9, 199
anova1 (Multi-sample tests for
vectors), 183
anova_propreg, 207
anova_propreg (Significance testing
for the coefficients of Quasi
binomial or the quasi Poisson
regression), 221
anova_qpois.reg, 12
anova_qpois.reg (Significance testing
for the coefficients of Quasi
binomial or the quasi Poisson
regression), 221
anova_quasipois.reg (ANOVA for two
quasi Poisson regression
models), 11
anovas, 114, 116
anovas (Many multi-sample tests), 125
ar1 (Estimation of an AR(1) model), 72
as_integer, 21, 244
as_integer (Check if values are
integers and convert to
integer), 20
auc, 74
auc (Many (and one) area aunder the
curve values), 111
Backward selection regression, 13
bc (Estimation of the Box-Cox
transformation), 73
bcdcor, 94
bcdcor (Distance correlation), 65
beta.mle, 82, 170, 180, 193, 194
INDEX
beta.mle (MLE of distributions defined
in the (0, 1) interval), 174
betaprime.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
BIC (using partial correlation)
forward regression, 14
BIC forward regression with
generalised linear models, 15
bic.corfsreg, 16
bic.corfsreg (BIC (using partial
correlation) forward
regression), 14
bic.fs.reg (BIC forward regression
with generalised linear
models), 15
Binary search algorithm, 16
binary_search, 79, 217
binary_search (Binary search
algorithm), 16
bincomb (Permutation), 202
binom.mle (MLE of count data
(univariate discrete
distributions)), 172
Binomial coefficient and its
logarithm, 17
block.anova (Multi-sample tests for
vectors), 183
block.anovas, 129
block.anovas (Many multi-sample tests),
125
boot.ttest2 (Bootstrap t-test for 2
independent samples), 18
Bootstrap t-test for 2 independent
samples, 18
borel.mle (MLE of count data
(univariate discrete
distributions)), 172
bs.reg (Backward selection regression),
13
btmprobs (Fitted probabilities of the
Terry-Bradley model), 80
cat.goftests (Many one sample goodness
of fit tests for categorical
data), 130
cauchy.mle (MLE of continuous
univariate distributions
267
defined on the real line), 171
Check if any column or row is fill
with zeros, 19
Check if values are integers and
convert to integer, 20
Check Namespace and Rd files, 21
Check whether a square matrix is
symmetric, 23
check_data (Search for variables with
zero range in a matrix), 220
checkAliases (Check Namespace and Rd
files), 21
checkExamples, 213
checkExamples (Check Namespace and Rd
files), 21
checkNamespace (Check Namespace and Rd
files), 21
checkRd, 213
checkTF (Check Namespace and Rd files),
21
chisq.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
cholesky, 24, 100
cholesky (Cholesky decomposition of a
square matrix), 24
Cholesky decomposition of a square
matrix, 24
Choose, 192, 216
Choose (Binomial coefficient and its
logarithm), 17
circlin.cor (Circular-linear
correlation), 27
Circular or angular regression, 25
Circular-linear correlation, 27
col.coxpoisrat (Cox confidence
interval for the ratio of two
Poisson variables), 57
col.yule, 254
col.yule (Column-wise Yule’s Y
(coefficient of colligation)),
51
colAll (Column and row-wise Any/All), 29
colanovas (Many Welch’s F-tests), 156
colAny (Column and row-wise Any/All), 29
colar1 (Estimation of an AR(1) model),
72
268
colaucs (Many (and one) area aunder
the curve values), 111
colCountValues (Row - Wise
matrix/vector count the
frequency of a value), 217
colcvs (Column and row wise
coefficients of variation), 28
coldiffs, 34, 35
coldiffs (Column-wise differences), 43
colexp2.mle (Column-wise MLE of some
univariate distributions), 47
colexpmle (Column-wise MLE of some
univariate distributions), 47
colFalse, 63, 109, 219
colFalse (Column-wise true/false
value), 49
colgammamle (Column-wise MLE of some
univariate distributions), 47
colgeom.mle (MLE for multivariate
discrete data), 166
colhameans (Column and row-wise means
of a matrix), 30
colinvgauss.mle (Column-wise MLE of
some univariate
distributions), 47
colkurtosis (Column-wise kurtosis and
skewness coefficients), 44
collaplace.mle (Column-wise MLE of
some univariate
distributions), 47
collindley.mle (Column-wise MLE of
some univariate
distributions), 47
colMads, 30, 162, 201, 238
colMads (Column and rows-wise mean
absolute deviations), 41
colmaxboltz.mle (Column-wise MLE of
some univariate
distributions), 47
colMaxs, 8, 35, 42, 218, 234, 247
colMaxs (Column-wise minimum and
maximum), 46
colMeans, 29, 31, 32, 38, 41
colmeans, 21, 38, 39, 41, 43, 44, 93, 97, 98,
110, 122, 187, 191, 195, 196, 201,
229, 231, 238, 242, 244, 251
colmeans (Column and row-wise means of
a matrix), 30
INDEX
colMedians, 20, 29, 30, 32, 34, 35, 38, 41, 42,
44, 47, 49, 67, 89, 93, 97, 162, 164,
165, 187, 196, 215, 218, 229, 231,
236, 240
colMedians (Column and row-wise
medians), 31
colMins, 8, 30, 35, 42, 163, 218, 234, 247
colMins (Column-wise minimum and
maximum), 46
colMinsMaxs (Column-wise minimum and
maximum), 46
colnormal.mle (Column-wise MLE of some
univariate distributions), 47
colnormlog.mle (Column-wise MLE of
some univariate
distributions), 47
colnth, 232
colnth (Column and row-wise nth
smallest value of a
matrix/vector), 32
colOrder (Column and row-wise Order Sort Indices), 33
colpareto.mle (Column-wise MLE of some
univariate distributions), 47
colPmax (Column-row wise minima and
maxima of two matrices), 42
colPmin (Column-row wise minima and
maxima of two matrices), 42
colpois.mle (Column-wise MLE of some
univariate distributions), 47
colpois.tests (Many tests for the
dispersion parameter in
Poisson distribution), 147
colpoisdisp.tests (Many tests for the
dispersion parameter in
Poisson distribution), 147
colpoisson.mle, 205
colpoisson.mle (MLE for multivariate
discrete data), 166
colprods, 34
colprods (Column and row-wise
products), 34
colrange, 8, 20, 41, 47, 49, 89, 164, 165, 174,
215, 221, 234, 240, 247
colrange (Column and row-wise range of
values of a matrix), 35
colRanks, 212
colRanks (Column and row-wise ranks), 36
INDEX
colrayleigh.mle (Column-wise MLE of
some univariate
distributions), 47
colrint.regbx, 124
colrint.regbx (Many random intercepts
LMMs for balanced data with a
single identical covariate.),
133
colrow.zero (Check if any column or
row is fill with zeros), 19
colShuffle, 39, 98, 244, 251
colShuffle (Column and row-wise
Shuffle), 37
colskewness, 97, 122, 187, 229
colskewness (Column-wise kurtosis and
skewness coefficients), 44
colsums, 28, 30, 34, 35, 71, 146, 239
colsums (Column and row-wise sums of a
matrix), 38
colTabulate, 46
colTabulate (Column and row-wise
tabulate), 39
colTrue, 63, 109, 219
colTrue (Column-wise true/false value),
49
colTrueFalse (Column-wise true/false
value), 49
Column and row wise coefficients of
variation, 28
Column and row-wise Any/All, 29
Column and row-wise means of a matrix,
30
Column and row-wise medians, 31
Column and row-wise nth smallest value
of a matrix/vector, 32
Column and row-wise Order - Sort
Indices, 33
Column and row-wise products, 34
Column and row-wise range of values of
a matrix, 35
Column and row-wise ranks, 36
Column and row-wise Shuffle, 37
Column and row-wise sums of a matrix,
38
Column and row-wise tabulate, 39
Column and row-wise variances and
standard deviations, 40
Column and rows-wise mean absolute
269
deviations, 41
Column-row wise minima and maxima of
two matrices, 42
Column-wise differences, 43
Column-wise kurtosis and skewness
coefficients, 44
Column-wise matching coefficients, 45
Column-wise minimum and maximum, 46
Column-wise MLE of some univariate
distributions, 47
Column-wise true/false value, 49
Column-wise uniformity Watson test
for circular data, 50
Column-wise Yule’s Y (coefficient of
colligation), 51
columns (Get specific columns/rows fo
a matrix), 89
colvarcomps.mle, 134, 183
colvarcomps.mle (Many moment and
maximum likelihood
estimations of variance
components), 123
colvarcomps.mom, 210
colvarcomps.mom (Many moment and
maximum likelihood
estimations of variance
components), 123
colVars, 20, 21, 28, 31, 35, 38, 39, 41, 44, 47,
49, 57, 71, 89, 93, 97, 98, 112, 146,
187, 191, 205, 215, 218, 221, 229,
231, 238–240, 242, 244, 251
colVars (Column and row-wise variances
and standard deviations), 40
colvm.mle (Column-wise MLE of some
univariate distributions), 47
colwatsons (Column-wise uniformity
Watson test for circular
data), 50
colweibull.mle (Column-wise MLE of
some univariate
distributions), 47
comb_n, 18, 203
comb_n (All k possible combinations
from n elements), 7
combn, 203
cor, 56, 57
cor.fbed, 202
cor.fbed (FBED variable selection
270
method using the correlation),
77
cor.fsreg, 13, 15, 16, 78, 85, 103, 105, 202
cor.fsreg (Correlation based forward
regression), 52
cora, 24, 228
cora (Covariance and correlation
matrix), 56
corpairs, 122
corpairs (Correlation between pairs of
variables), 53
Correlation based forward regression,
52
Correlation between pairs of
variables, 53
Correlations, 55
correls, 37, 54, 58, 71, 74, 78, 86, 105, 121,
127, 146, 151–153, 157, 160, 202,
212, 228, 239
correls (Correlations), 55
count_value (Row - Wise matrix/vector
count the frequency of a
value), 217
countNA (Row - Wise matrix/vector
count the frequency of a
value), 217
cov, 57
cova, 24, 100, 251
cova (Covariance and correlation
matrix), 56
Covariance and correlation matrix, 56
Cox confidence interval for the ratio
of two Poisson variables, 57
cox.poisrat (Cox confidence interval
for the ratio of two Poisson
variables), 57
cqtest (Multi-sample tests for
vectors), 183
cqtests (Many non parametric
multi-sample tests), 128
Cross-Validation for the k-NN
algorithm, 58
ct.mle (MLE of continuous univariate
distributions defined on the
real line), 171
data.frame.to_matrix, 60, 227
dcor, 68
dcor (Distance correlation), 65
INDEX
dcor.ttest, 65, 66
dcor.ttest (Hypothesis test for the
distance correlation), 93
dcov, 66, 94
dcov (Distance variance and
covariance), 67
Density of the multivariate normal and
t distributions, 61
Design Matrix, 62
design_matrix (Design Matrix), 62
Diag.fill, 201
Diag.fill (Diagonal Matrix), 63
Diag.matrix (Diagonal Matrix), 63
Diagonal Matrix, 63
Digamma (Natural logarithm of the
gamma function and its
derivatives), 193
diri.nr2, 175, 178, 180, 193, 194
diri.nr2 (Fitting a Dirichlet
distribution via
Newton-Rapshon), 81
dirimultinom.mle (MLE for multivariate
discrete data), 166
dirknn (k-NN algorithm using the arc
cosinus distance), 103
Dist, 43, 60, 65, 70, 195, 201, 241
Dist (Distance matrix), 66
dista, 43, 60, 67, 70, 110, 195, 201, 241
dista (Distance between vectors and a
matrix), 64
Distance between vectors and a matrix,
64
Distance correlation, 65
Distance matrix, 66
Distance variance and covariance, 67
dmvnorm, 179
dmvnorm (Density of the multivariate
normal and t distributions), 61
dmvt (Density of the multivariate
normal and t distributions), 61
dvar, 70
dvar (Distance variance and
covariance), 67
eachcol.apply (Operations between two
matrices or matrix and
vector), 200
eachrow (Operations between two
matrices or matrix and
INDEX
vector), 200
edist, 66, 68, 94
edist (Energy distance between
matrices), 70
eel.test1 (One sample empirical and
exponential empirical
likelihood test), 197
eel.test2 (Two sample exponential
empirical likelihood test), 248
Eigenvalues and eigenvectors in high
dimensional principal
component analysis, 68
el.test1 (One sample empirical and
exponential empirical
likelihood test), 197
Energy distance between matrices, 70
Equality of objects, 71
Estimation of an AR(1) model, 72
Estimation of the Box-Cox
transformation, 73
exp2.mle (MLE of continuous univariate
distributions defined on the
positive line), 169
expmle (MLE of continuous univariate
distributions defined on the
positive line), 169
Exponential empirical likelihood for
a one sample mean vector
hypothesis testing, 74
Exponential empirical likelihood
hypothesis testing for two
mean vectors, 75
expregs (Many exponential regressions),
117
FBED variable selection method using
the correlation, 77
Find element, 78
Find the given value in a hash table,
79
fish.kent (Hypothesis test for von
Mises-Fisher distribution
over Kent distribution), 95
Fitted probabilities of the
Terry-Bradley model, 80
Fitting a Dirichlet distribution via
Newton-Rapshon, 81
floyd, 246
floyd (Floyd-Warshall algorithm), 82
271
Floyd-Warshall algorithm, 82
foldnorm.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
Forward selection with generalised
linear regression models, 84
freq.max (minimum and maximum
frequencies), 165
freq.min (minimum and maximum
frequencies), 165
fs.reg, 13, 16, 78, 103, 202
fs.reg (Forward selection with
generalised linear regression
models), 84
ftest, 19, 95, 123, 198
ftest (Multi-sample tests for vectors),
183
ftests, 9, 111, 112, 114, 116, 118, 119, 129,
131, 132, 140, 149, 157, 159, 185,
249
ftests (Many multi-sample tests), 125
G-square test of conditional
indepdence, 85
g2Test, 10, 121, 160, 197, 227, 228
g2Test (G-square test of conditional
indepdence), 85
g2Test_perm, 121, 160
g2Test_perm (G-square test of
conditional indepdence), 85
g2Test_univariate, 85, 86, 130, 159, 228
g2Test_univariate (Matrix with
G-square tests of
indepedence), 159
g2Test_univariate_perm, 85, 86
g2Test_univariate_perm (Matrix with
G-square tests of
indepedence), 159
g2tests, 81, 115
g2tests (Many G-square tests of
indepedence), 119
g2tests_perm (Many G-square tests of
indepedence), 119
gammamle, 48, 172, 181
gammamle (MLE of continuous univariate
distributions defined on the
positive line), 169
gammanb (Naive Bayes classifiers), 189
272
gammanb.pred (Prediction with some
naive Bayes classifiers), 204
Gaussian regression with a log-link, 87
gaussian.nb, 179, 205
gaussian.nb (Naive Bayes classifiers),
189
gaussiannb.pred (Prediction with some
naive Bayes classifiers), 204
Generates random values from a normal
and puts them in a matrix, 88
geom.anova (Analysis of variance with
a count variable), 9
geom.anovas (Many analysis of variance
tests with a discrete
variable), 114
geom.mle (MLE of count data
(univariate discrete
distributions)), 172
geom.nb (Naive Bayes classifiers), 189
geom.regs (Many simple geometric
regressions), 143
geomnb.pred (Prediction with some
naive Bayes classifiers), 204
Get specific columns/rows fo a matrix,
89
ginis (Many Gini coefficients), 121
glm_logistic, 85, 186
glm_logistic (Logistic and Poisson
regression models), 105
glm_poisson, 85
glm_poisson (Logistic and Poisson
regression models), 105
group.all (Some summary statistics of
a vector for each level of a
grouping variable), 230
group.any (Some summary statistics of
a vector for each level of a
grouping variable), 230
group.mad (Some summary statistics of
a vector for each level of a
grouping variable), 230
group.max (Some summary statistics of
a vector for each level of a
grouping variable), 230
group.mean (Some summary statistics of
a vector for each level of a
grouping variable), 230
group.med (Some summary statistics of
INDEX
a vector for each level of a
grouping variable), 230
group.min (Some summary statistics of
a vector for each level of a
grouping variable), 230
group.min_max (Some summary statistics
of a vector for each level of
a grouping variable), 230
group.sum, 231
group.sum (Sums of a vector for each
level of a grouping variable),
242
group.var (Some summary statistics of
a vector for each level of a
grouping variable), 230
groupcolVars, 231
groupcolVars (Column and row-wise
variances and standard
deviations), 40
groupcorrels (Correlations), 55
gumbel.mle (MLE of continuous
univariate distributions
defined on the real line), 171
halfnorm.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
Hash - Pair function, 90
Hash object to a list object, 91
hash.find, 90, 91
hash.find (Find the given value in a
hash table), 79
hash.list, 80, 91
hash.list (Hash - Pair function), 90
hash2list (Hash object to a list
object), 91
hd.eigen (Eigenvalues and eigenvectors
in high dimensional principal
component analysis), 68
High dimensional MCD based detection
of outliers, 92
hsecant01.mle (MLE of distributions
defined in the (0, 1)
interval), 174
Hypothesis test for the distance
correlation, 93
Hypothesis test for two means of
percentages, 94
INDEX
Hypothesis test for von Mises-Fisher
distribution over Kent
distribution, 95
Hypothesis testing betseen two
skewness or kurtosis
coefficients, 96
iag.mle, 26, 61, 96, 142, 226
iag.mle (MLE of (hyper-)spherical
distributions), 167
ibeta.mle (MLE of distributions
defined in the (0, 1)
interval), 174
Index of the columns of a data.frame
which are factor variables, 97
Insert new function names in the
NAMESPACE file, 98
invdir.mle (MLE of the inverted
Dirichlet distribution), 177
Inverse of a symmetric positive
definite matrix, 99
invgauss.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
is.symmetric, 25, 61
is.symmetric (Check whether a square
matrix is symmetric), 23
is_element, 17
is_element (Find element), 78
is_integer, 244
is_integer (Check if values are
integers and convert to
integer), 20
james, 75, 77
james (James multivariate version of
the t-test), 100
James multivariate version of the
t-test, 100
k nearest neighbours algorithm (k-NN),
101
k-NN algorithm using the arc cosinus
distance, 103
knn, 60, 104
knn (k nearest neighbours algorithm
(k-NN)), 101
273
knn.cv (Cross-Validation for the k-NN
algorithm), 58
kruskaltest (Multi-sample tests for
vectors), 183
kruskaltests (Many non parametric
multi-sample tests), 128
kuiper (Uniformity test for circular
data), 249
kurt (Skewness and kurtosis
coefficients), 229
kurt.test2 (Hypothesis testing betseen
two skewness or kurtosis
coefficients), 96
laplace.mle (MLE of continuous
univariate distributions
defined on the real line), 171
Lbeta, 18, 192
Lbeta (Natural logarithm of the beta
function), 192
Lchoose, 192, 216
Lchoose (Binomial coefficient and its
logarithm), 17
Lgamma, 18, 193
Lgamma (Natural logarithm of the gamma
function and its derivatives),
193
lindley.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
Linear models for large scale data, 104
list.ftests (Many F-tests with really
huge matrices), 118
lm, 105
lm.fit, 105
lmfit (Linear models for large scale
data), 104
Log, 216
Log (Natural Logarithm each element of
a matrix), 191
logcauchy.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
Logistic and Poisson regression
models, 105
Logistic or Poisson regression with a
single categorical predictor,
274
107
logistic.cat1, 10
logistic.cat1 (Logistic or Poisson
regression with a single
categorical predictor), 107
logistic.mle (MLE of continuous
univariate distributions
defined on the real line), 171
logistic_only, 15, 16, 53, 85, 88, 103, 106,
108, 118, 137, 139, 145, 151, 154,
156, 186, 207, 222, 253
logistic_only (Many univariate simple
binary logistic regressions),
151
logitnorm.mle (MLE of distributions
defined in the (0, 1)
interval), 174
loglogistic.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
lognorm.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
logseries.mle (MLE of count data
(univariate discrete
distributions)), 172
lomax.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
Lower and Upper triangular of a
matrix, 108
lower_tri (Lower and Upper triangular
of a matrix), 108
mad2 (Mean - Median absolute deviation
of a vector), 161
mahala, 65
mahala (Mahalanobis distance), 110
Mahalanobis distance, 110
Many (and one) area aunder the curve
values, 111
Many 2 sample proportions tests, 112
Many 2 sample tests, 113
Many analysis of variance tests with a
discrete variable, 114
Many ANCOVAs, 116
INDEX
Many exponential regressions, 117
Many F-tests with really huge
matrices, 118
Many G-square tests of indepedence, 119
Many Gini coefficients, 121
Many hypothesis tests for two means of
percentages, 122
Many moment and maximum likelihood
estimations of variance
components, 123
Many multi-sample tests, 125
Many multivariate simple linear
regressions coefficients, 127
Many non parametric multi-sample
tests, 128
Many odds ratio tests, 129
Many one sample goodness of fit tests
for categorical data, 130
Many one sample tests, 131
Many random intercepts LMMs for
balanced data with a single
identical covariate., 133
Many regression based tests for single
sample repeated measures, 134
Many score based GLM regressions, 136
Many score based regression models, 138
Many Shapiro-Francia normality tests,
139
Many simple circular or angular
regressions, 141
Many simple Gaussian regressions with
a log-link, 142
Many simple geometric regressions, 143
Many simple linear mixed model
regressions, 144
Many simple linear regressions
coefficients, 145
Many simple multinomial regressions,
146
Many tests for the dispersion
parameter in Poisson
distribution, 147
Many two-way ANOVAs, 148
Many univariate generalised linear
models, 149
Many univariate simple binary
logistic regressions, 151
Many univariate simple linear
INDEX
regressions, 152
Many univariate simple poisson
regressions, 154
Many univariate simple quasi poisson
regressions, 155
Many Welch’s F-tests, 156
mat.mat (Number of equal columns
between two matrices), 195
Match, 61, 71, 97, 157, 196, 239
match, 158
match.coefs (Column-wise matching
coefficients), 45
Matrix with all pairs of t-tests, 158
Matrix with G-square tests of
indepedence, 159
matrix.sum (Sum of a matrix), 240
matrnorm, 225
matrnorm (Generates random values from
a normal and puts them in a
matrix), 88
maxboltz.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
mcnemar (Multi-sample tests for
vectors), 183
mcnemars (Many 2 sample tests), 113
Mean - Median absolute deviation of a
vector, 161
med, 29, 31, 32, 38, 162, 217, 242
med (Median of a vector), 162
Median of a vector, 162
mediandir (Spherical and
hyperspherical median), 237
min_max (minimum and maximum), 164
Minima and maxima of two
vectors/matrices, 163
minimum and maximum, 164
minimum and maximum frequencies, 165
MLE for multivariate discrete data, 166
MLE of (hyper-)spherical
distributions, 167
MLE of continuous univariate
distributions defined on the
positive line, 169
MLE of continuous univariate
distributions defined on the
real line, 171
275
MLE of count data (univariate discrete
distributions), 172
MLE of distributions defined in the
(0, 1) interval, 174
MLE of some circular distributions, 176
MLE of the inverted Dirichlet
distribution, 177
MLE of the multivariate normal
distribution, 178
MLE of the ordinal model without
covariates, 179
MLE of the tobit model, 180
model.matrix, 62
Moment and maximum likelihood
estimation of variance
components, 181
Multi-sample tests for vectors, 183
multinom.mle, 178, 179
multinom.mle (MLE for multivariate
discrete data), 166
multinom.nb (Naive Bayes classifiers),
189
multinom.reg (Multinomial regression),
185
multinom.regs (Many simple multinomial
regressions), 146
Multinomial regression, 185
multinomnb.pred (Prediction with some
naive Bayes classifiers), 204
Multivariate kurtosis, 186
Multivariate Laplace random values
simulation, 187
Multivariate normal and t random
values simulation, 188
multivmf.mle (MLE of (hyper-)spherical
distributions), 167
mv.eeltest1, 77
mv.eeltest1 (Exponential empirical
likelihood for a one sample
mean vector hypothesis
testing), 74
mv.eeltest2, 75, 101
mv.eeltest2 (Exponential empirical
likelihood hypothesis testing
for two mean vectors), 75
mvbetas, 54, 71, 105, 146, 153, 239
mvbetas (Many multivariate simple
linear regressions
276
coefficients), 127
mvkurtosis (Multivariate kurtosis), 186
mvnorm.mle, 61
mvnorm.mle (MLE of the multivariate
normal distribution), 178
Naive Bayes classifiers, 189
Natural Logarithm each element of a
matrix, 191
Natural logarithm of the beta
function, 192
Natural logarithm of the gamma
function and its derivatives,
193
negbin.mle, 148, 167, 245
negbin.mle (MLE of count data
(univariate discrete
distributions)), 172
Norm (Norm of a matrix), 194
Norm of a matrix, 194
normal.mle, 48, 170, 181
normal.mle (MLE of continuous
univariate distributions
defined on the real line), 171
normlog.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
normlog.reg, 143
normlog.reg (Gaussian regression with
a log-link), 87
normlog.regs, 87
normlog.regs (Many simple Gaussian
regressions with a log-link),
142
nth, 8, 20, 35, 47, 49, 63, 89, 97, 109, 162,
164, 165, 215, 217–219, 232, 234,
240, 247
nth (Column and row-wise nth smallest
value of a matrix/vector), 32
Number of equal columns between two
matrices, 195
odds, 46, 51, 197
odds (Many odds ratio tests), 129
Odds ratio and relative risk, 196
odds.ratio, 130, 254
odds.ratio (Odds ratio and relative
risk), 196
INDEX
omp (Orthogonal matching pursuit
regression), 201
ompr, 78
ompr (Orthogonal matching pursuit
regression), 201
One sample empirical and exponential
empirical likelihood test, 197
One sample t-test for a vector, 198
Operations between two matrices or
matrix and vector, 200
Order, 217
Order (Column and row-wise Order Sort Indices), 33
ordinal.mle (MLE of the ordinal model
without covariates), 179
Orthogonal matching pursuit
regression, 201
pareto.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
pc.skel, 204, 246
pc.skel (Skeleton of the PC algorithm),
227
percent.ttest (Hypothesis test for two
means of percentages), 94
percent.ttests (Many hypothesis tests
for two means of percentages),
122
permcor (Permutation based p-value for
the Pearson correlation
coefficient), 203
Permutation, 202
permutation, 61
permutation (Permutation), 202
Permutation based p-value for the
Pearson correlation
coefficient, 203
Pmax (Minima and maxima of two
vectors/matrices), 163
Pmin (Minima and maxima of two
vectors/matrices), 163
Pmin_Pmax (Minima and maxima of two
vectors/matrices), 163
pois.test (Tests for the dispersion
parameter in Poisson
distribution), 244
INDEX
poisdisp.test (Tests for the
dispersion parameter in
Poisson distribution), 244
poisson.anova, 81, 108, 115, 148, 245
poisson.anova (Analysis of variance
with a count variable), 9
poisson.anovas, 10, 108, 148, 245
poisson.anovas (Many analysis of
variance tests with a
discrete variable), 114
poisson.cat1 (Logistic or Poisson
regression with a single
categorical predictor), 107
poisson.mle, 10, 48, 81, 115, 148, 167, 245
poisson.mle (MLE of count data
(univariate discrete
distributions)), 172
poisson.nb, 167
poisson.nb (Naive Bayes classifiers),
189
poisson_only, 10, 15, 16, 53, 81, 85, 106,
108, 115, 118, 137, 139, 144, 147,
148, 151, 152, 156, 174, 208, 245,
253
poisson_only (Many univariate simple
poisson regressions), 154
poissonnb.pred (Prediction with some
naive Bayes classifiers), 204
Prediction with some naive Bayes
classifiers, 204
prop.reg, 94, 95, 122, 123, 208, 222
prop.reg (Quasi binomial regression
for proportions), 205
prop.regs, 87, 143, 144, 147
prop.regs (Quasi binomial regression
for proportions), 205
proptest (Many one sample tests), 131
proptests (Many 2 sample proportions
tests), 112
qpois.reg, 12, 222
qpois.reg (Quasi Poisson regression
for count data), 207
qpois.regs (Quasi Poisson regression
for count data), 207
Quasi binomial regression for
proportions, 205
Quasi Poisson regression for count
data, 207
277
quasi.poisson_only (Many univariate
simple quasi poisson
regressions), 155
quasipoisson.anova, 12
quasipoisson.anova (Analysis of
variance with a count
variable), 9
quasipoisson.anovas (Many analysis of
variance tests with a
discrete variable), 114
racg, 168, 188, 189
racg (Angular central Gaussian random
values simulation), 10
Random intercepts linear mixed models,
209
Random values simulation from a von
Mises distribution, 210
Rank, 37
Rank (Ranks of the values of a vector),
211
Ranks of the values of a vector, 211
rayleigh.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
rbing, 224
rbing (Simulation of random values
from a Bingham distribution),
222
rbingham (Simulation of random values
from a Bingham distribution
with any symmetric matrix), 223
read.directory, 21, 23, 98, 235, 244
read.directory (Reading the files of a
directory), 212
read.examples, 23
read.examples (Reading the files of a
directory), 212
Reading the files of a directory, 212
regression, 15, 16, 53, 105, 106, 118, 137,
139, 151, 152, 154, 156, 157, 253
regression (Many univariate simple
linear regressions), 152
rel.risk (Odds ratio and relative
risk), 196
rep_col (Replicate columns/rows), 215
rep_row (Replicate columns/rows), 215
Repeated measures anova, 214
278
Replicate columns/rows, 215
Rfast-package, 6
rint.mle (Moment and maximum
likelihood estimation of
variance components), 181
rint.reg, 134, 136, 145, 183, 214
rint.reg (Random intercepts linear
mixed models), 209
rint.regbx, 133, 134, 136, 183
rint.regbx (Random intercepts linear
mixed models), 209
rint.regs (Many simple linear mixed
model regressions), 144
rm.anova (Repeated measures anova), 214
rm.anovas, 73, 214
rm.anovas (Many regression based tests
for single sample repeated
measures), 134
rm.lines, 73, 134, 210
rm.lines (Many regression based tests
for single sample repeated
measures), 134
rmdp, 69
rmdp (High dimensional MCD based
detection of outliers), 92
rmvlaplace, 11, 189
rmvlaplace (Multivariate Laplace
random values simulation), 187
rmvnorm, 11, 61, 88, 188, 225
rmvnorm (Multivariate normal and t
random values simulation), 188
rmvt, 11, 61, 188, 189
rmvt (Multivariate normal and t random
values simulation), 188
Rnorm, 88
Rnorm (Simulation of random values
from a normal distribution),
224
Round, 232
Round (Round each element of a
matrix/vector), 216
Round each element of a matrix/vector,
216
Row - Wise matrix/vector count the
frequency of a value, 217
Row-wise minimum and maximum, 218
Row-wise true value, 219
rowAll (Column and row-wise Any/All), 29
INDEX
rowAny (Column and row-wise Any/All), 29
rowCountValues (Row - Wise
matrix/vector count the
frequency of a value), 217
rowcvs (Column and row wise
coefficients of variation), 28
rowFalse, 20, 49, 89, 215, 240
rowFalse (Row-wise true value), 219
rowhameans (Column and row-wise means
of a matrix), 30
rowMads, 201
rowMads (Column and rows-wise mean
absolute deviations), 41
rowMaxs, 35, 47, 164, 165
rowMaxs (Row-wise minimum and maximum),
218
rowmeans (Column and row-wise means of
a matrix), 30
rowMedians, 41, 63, 109, 219
rowMedians (Column and row-wise
medians), 31
rowMins, 20, 35, 47, 49, 63, 89, 109, 164, 165,
215, 219, 240
rowMins (Row-wise minimum and maximum),
218
rowMinsMaxs (Row-wise minimum and
maximum), 218
rownth, 232
rownth (Column and row-wise nth
smallest value of a
matrix/vector), 32
rowOrder (Column and row-wise Order Sort Indices), 33
rowprods (Column and row-wise
products), 34
rowrange, 63, 109, 218, 219
rowrange (Column and row-wise range of
values of a matrix), 35
rowRanks (Column and row-wise ranks), 36
rows (Get specific columns/rows fo a
matrix), 89
rowShuffle (Column and row-wise
Shuffle), 37
rowsums, 30
rowsums (Column and row-wise sums of a
matrix), 38
rowTabulate (Column and row-wise
tabulate), 39
INDEX
rowTrue, 20, 49, 89, 215, 240
rowTrue (Row-wise true value), 219
rowTrueFalse (Row-wise true value), 219
rowVars, 63, 109, 219
rowVars (Column and row-wise variances
and standard deviations), 40
rvmf, 88, 168, 177, 211, 223–225
rvmf (Simulation of random values from
a von Mises-Fisher
distribution), 225
rvonmises, 50, 88, 177, 225, 226, 250
rvonmises (Random values simulation
from a von Mises
distribution), 210
score.betaregs (Many score based
regression models), 138
score.expregs (Many score based
regression models), 138
score.gammaregs (Many score based
regression models), 138
score.geomregs, 144, 147
score.geomregs (Many score based
regression models), 138
score.glms, 15, 16, 53, 87, 118, 139, 143,
145, 207, 208, 222
score.glms (Many score based GLM
regressions), 136
score.invgaussregs (Many score based
regression models), 138
score.multinomregs, 186
score.multinomregs (Many score based
GLM regressions), 136
score.negbinregs (Many score based GLM
regressions), 136
score.weibregs (Many score based
regression models), 138
score.ztpregs (Many score based
regression models), 138
Search for variables with zero range
in a matrix, 220
sftest (Many Shapiro-Francia normality
tests), 139
sftests, 44, 88
sftests (Many Shapiro-Francia
normality tests), 139
Significance testing for the
coefficients of Quasi
279
binomial or the quasi Poisson
regression, 221
Simulation of random values from a
Bingham distribution, 222
Simulation of random values from a
Bingham distribution with any
symmetric matrix, 223
Simulation of random values from a
normal distribution, 224
Simulation of random values from a von
Mises-Fisher distribution, 225
Skeleton of the PC algorithm, 227
skew, 44, 97
skew (Skewness and kurtosis
coefficients), 229
skew.test2, 44, 187, 229
skew.test2 (Hypothesis testing betseen
two skewness or kurtosis
coefficients), 96
Skewness and kurtosis coefficients, 229
Some summary statistics of a vector
for each level of a grouping
variable, 230
Sort, 42, 163
Sort (Sort - Sort a vector
coresponding to another), 231
Sort - Sort a vector coresponding to
another, 231
Sort and unique numbers, 233
sort_cor_vectors, 233, 234
sort_cor_vectors (Sort - Sort a vector
coresponding to another), 231
sort_mat, 20, 35, 42, 47, 49, 63, 83, 89, 109,
163–165, 215, 218, 219, 233, 240
sort_mat (Sorting of the columns-rows
of a matrix), 234
sort_unique, 232, 234
sort_unique (Sort and unique numbers),
233
Sorting of the columns-rows of a
matrix, 234
Source many R files, 235
sourceR, 23, 213
sourceR (Source many R files), 235
sourceRd, 23, 213
sourceRd (Source many R files), 235
spat.med (Spatial median for Euclidean
data), 236
280
Spatial median for Euclidean data, 236
spdinv (Inverse of a symmetric
positive definite matrix), 99
Spherical and hyperspherical median,
237
spml.mle, 26, 104, 142
spml.mle (MLE of some circular
distributions), 176
spml.reg, 27
spml.reg (Circular or angular
regression), 25
spml.regs (Many simple circular or
angular regressions), 141
squareform (Vector allocation in a
symmetric matrix), 251
Standardisation, 238
standardise (Standardisation), 238
Sub-matrix, 239
submatrix (Sub-matrix), 239
Sum of a matrix, 240
Sum of all pairwise distances in a
distance matrix, 240
Sums of a vector for each level of a
grouping variable, 242
Table, 58
Table (Table Creation - Frequency of
each value), 243
Table Creation - Frequency of each
value, 243
Tests for the dispersion parameter in
Poisson distribution, 244
tmle (MLE of continuous univariate
distributions defined on the
real line), 171
tobit.mle (MLE of the tobit model), 180
Topological sort of a DAG, 246
topological_sort (Topological sort of
a DAG), 246
total.dist, 65, 70
total.dist (Sum of all pairwise
distances in a distance
matrix), 240
total.dista, 65, 70
total.dista (Sum of all pairwise
distances in a distance
matrix), 240
transpose (Transpose of a matrix), 247
Transpose of a matrix, 247
INDEX
Trigamma (Natural logarithm of the
gamma function and its
derivatives), 193
ttest, 111, 114, 131, 140, 159, 199, 249
ttest (Many one sample tests), 131
ttest1, 198
ttest1 (One sample t-test for a
vector), 198
ttest2, 19, 95, 123
ttest2 (Multi-sample tests for
vectors), 183
ttests, 9, 111, 112, 116, 119, 126, 131, 132,
140, 149, 159, 185, 199, 249
ttests (Many 2 sample tests), 113
ttests.pairs (Matrix with all pairs of
t-tests), 158
Two sample exponential empirical
likelihood test, 248
twoway.anova (Multi-sample tests for
vectors), 183
twoway.anovas (Many two-way ANOVAs), 148
Uniformity test for circular data, 249
univglms, 12, 13, 15, 16, 53, 55, 71, 86, 106,
118, 121, 127, 137, 139, 145, 146,
153, 154, 156, 160, 207, 208, 222,
239, 253
univglms (Many univariate generalised
linear models), 149
univglms2 (Many univariate generalised
linear models), 149
upper_tri (Lower and Upper triangular
of a matrix), 108
Var, 242
Var (Variance of a vector), 250
var2test (Multi-sample tests for
vectors), 183
var2tests (Many 2 sample tests), 113
varcomps.mle, 73, 124, 136, 214
varcomps.mle (Moment and maximum
likelihood estimation of
variance components), 181
varcomps.mom, 134, 210
varcomps.mom (Moment and maximum
likelihood estimation of
variance components), 181
Variance of a vector, 250
vartest (Many one sample tests), 131
INDEX
vartests (Many multi-sample tests), 125
vecdist (Distance matrix), 66
Vector allocation in a symmetric
matrix, 251
vm.mle, 48, 168, 172, 211
vm.mle (MLE of some circular
distributions), 176
vmf.mle, 50, 96, 104, 177, 226, 238, 250
vmf.mle (MLE of (hyper-)spherical
distributions), 167
watson, 50
watson (Uniformity test for circular
data), 249
weib.reg (Weibull regression model), 252
Weibull regression model, 252
weibull.mle (MLE of continuous
univariate distributions
defined on the positive line),
169
which_isFactor (Index of the columns
of a data.frame which are
factor variables), 97
wigner.mle (MLE of continuous
univariate distributions
defined on the real line), 171
wrapcauchy.mle (MLE of some circular
distributions), 176
XopY.sum (Operations between two
matrices or matrix and
vector), 200
yule, 51
yule (Yule’s Y (coefficient of
colligation)), 253
Yule’s Y (coefficient of colligation),
253
zip.mle, 167, 170, 172
zip.mle (MLE of count data (univariate
discrete distributions)), 172
ztp.mle, 167
ztp.mle (MLE of count data (univariate
discrete distributions)), 172
281
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