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Compositional (version 3.4)

Compositional Data Analysis

Description

Regression, classification, contour plots, hypothesis testing and fitting of distributions for compositional data are some of the functions included. The standard textbook for such data is John Aitchison's (1986) "The statistical analysis of compositional data". Relevant papers include a) Tsagris M.T., Preston S. and Wood A.T.A. (2011) A data-based power transformation for compositional data. Fourth International International Workshop on Compositional Data Analysis. b) Tsagris M. (2014). The k-NN algorithm for compositional data: a revised approach with and without zero values present. Journal of Data Science, 12(3):519--534. c) Tsagris M. (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2):47--57. d) Tsagris M., Preston S. and Wood A.T.A. (2016). Improved supervised classification for compositional data using the alpha-transformation. Journal of Classification, 33(2):243--261. e) 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. f) Tsagris M. and Stewart C. (2018). A Dirichlet regression model for compositional data with zeros. Lobachevskii Journal of Mathematics, 39(3): 398--412. Furher, we include functions for percentages (or proportions).

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Version

Install

install.packages('Compositional')

Monthly Downloads

1,183

Version

3.4

License

GPL (>= 2)

Maintainer

Michail Tsagris

Last Published

March 12th, 2019

Functions in Compositional (3.4)

Estimation of the value of alpha via the profile log-likelihood

Estimation of the value of \(\alpha\) via the alfa profile log-likelihood
Cross validation for the regularised discriminant analysis with compositional data using the alpha-transformation

Cross validation for the regularised discriminant analysis with compositional data using the \(\alpha\)-transformation
MLE of distributions defined in the (0, 1) interval

MLE of distributions defined in the (0, 1) interval
Mixture model selection via BIC

Mixture model selection via BIC
Tuning the value of alpha in the alpha-regression

Tuning the value of \(\alpha\) in the \(\alpha\)-regression
k-NN regression with compositional data

k-NN regression with compositional data
Hypothesis testing for two or more compositional mean vectors

Hypothesis testing for two or more compositional mean vectors
Projection pursuit regression for compositional data

Projection pursuit regression for compositional data
Multivariate regression with compositional data

Multivariate regression with compositional data
Exponential empirical likelihood hypothesis testing for two mean vectors

Exponential empirical likelihood hypothesis testing for two mean vectors
Empirical likelihood for a one sample mean vector hypothesis testing

Empirical likelihood for a one sample mean vector hypothesis testing
Helper functions for the Kullback-Leibler regression

Helper functions for the Kullback-Leibler regression
Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions

Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions
Contour plot of a Dirichlet distribution in S^2

Contour plot of a Dirichlet distribution in \(S^2\)
Contour plot of a Gaussian mixture model in S^2

Contour plot of a Gaussian mixture model in \(S^2\)
The Helmert sub-matrix

The Helmert sub-matrix
Fitting a Dirichlet distribution

Fitting a Dirichlet distribution
Hotelling's multivariate version of the 1 sample t-test for Euclidean data

Hotelling's multivariate version of the 1 sample t-test for Euclidean data
Tuning of the principal components regression

Tuning of the principal components regression
Perturbation operation

Perturbation operation
Regression with compositional data using the alpha-transformation

Regression with compositional data using the \(\alpha\)-transformation
Simulation of compositional data from Gaussian mixture models

Simulation of compositional data from Gaussian mixture models
Multivariate kernel density estimation

Multivariate kernel density estimation
Ridge regression with compositional data in the covariates side using the alpha-transformation

Ridge regression with compositional data in the covariates side using the \(\alpha\)-transformation
Contour plot of the skew skew-normal distribution in S^2

Contour plot of the skew skew-normal distribution in \(S^2\)
Multivariate normal random values simulation on the simplex

Multivariate normal random values simulation on the simplex
Multivariate skew normal random values simulation on the simplex

Multivariate skew normal random values simulation on the simplex
Zero adjusted Dirichlet regression

Zero adjusted Dirichlet regression
MLE of the folded model for a given value of alpha

MLE of the folded model for a given value of \(\alpha\)
The additive log-ratio transformation and its inverse

The additive log-ratio transformation and its inverse
Contour plot of the t distribution in S^2

Contour plot of the t distribution in \(S^2\)
Estimating location and scatter parameters for compositional data

Estimating location and scatter parameters for compositional data
Empirical likelihood hypothesis testing for two mean vectors

Empirical likelihood hypothesis testing for two mean vectors
The Frechet mean for compositional data

The Frechet mean for compositional data
Principal component generalised linear models

Principal component generalised linear models
Tuning the principal components with GLMs

Tuning the principal components with GLMs
MLE for the multivarite t distribution

MLE for the multivarite t distribution
Compositional-package

Compositional Data Analysis
Contour plot of the normal distribution in S^2

Contour plot of the normal distribution in \(S^2\)
Ridge regression

Ridge regression
Cross validation for the ridge regression

Cross validation for the ridge regression
Estimation of the value of alpha in the folded model

Estimation of the value of \(\alpha\) in the folded model
Ternary diagram

Ternary diagram
Total variability

Total variability
Inverse of the alpha-transformation

Inverse of the \(\alpha\)-transformation
The alpha-transformation

The \(\alpha\)-transformation
Fast estimation of the value of alpha

Fast estimation of the value of \(\alpha\)
The alpha-distance

The \(\alpha\)-distance
Tuning the number of PCs in the PCR with compositional data using the alpha-transformation

Tuning the number of PCs in the PCR with compositional data using the \(\alpha\)-transformation
Tuning of the k-NN algorithm for compositional data

Tuning of the he k-NN algorithm for compositional data
Multivariate or univariate regression with compositional data in the covariates side using the alpha-transformation

Multivariate or univariate regression with compositional data in the covariates side using the \(\alpha\)-transformation
Ridge regression with the alpha-transformation plot

Ridge regression plot
Cross validation for the ridge regression with compositional data as predictor using the alpha-transformation

Cross validation for the ridge regression with compositional data as predictor using the \(\alpha\)-transformation
Contour plot of the kernel density estimate in S^2

Contour plot of the kernel density estimate in \(S^2\)
The k-NN algorithm for compositional data

The k-NN algorithm for compositional data
Log-likelihood ratio test for a Dirichlet mean vector

Log-likelihood ratio test for a Dirichlet mean vector
Density values of a Dirichlet distribution

Density values of a Dirichlet distribution
Exponential empirical likelihood for a one sample mean vector hypothesis testing

Exponential empirical likelihood for a one sample mean vector hypothesis testing
Hotelling's multivariate version of the 2 sample t-test for Euclidean data

Hotelling's multivariate version of the 2 sample t-test for Euclidean data
Fitting a Dirichlet distribution via Newton-Rapshon

Fitting a Dirichlet distribution via Newton-Rapshon
Dirichlet regression

Dirichlet regression
Divergence based regression for compositional data with compositional data in the covariates side using the alpha-transformation

Divergence based regression for compositional data with compositional data in the covariates side using the \(\alpha\)-transformation
James multivariate version of the t-test

James multivariate version of the t-test
Multivariate analysis of variance (James test)

Multivariate analysis of variance (James test)
Divergence based regression for compositional data

Divergence based regression for compositional data
Gaussian mixture models for compositional data

Gaussian mixture models for compositional data
Tuning of the bandwidth h of the kernel using the maximum likelihood cross validation

Tuning of the bandwidth h of the kernel using the maximum likelihood cross validation
Multivariate t random values simulation on the simplex

Multivariate t random values simulation on the simplex
Multivariate linear regression

Multivariate linear regression
Regularised discriminant analysis for Euclidean data

Regularised discriminant analysis for Euclidean data
Tuning the parameters of the regularised discriminant analysis

Tuning the parameters of the regularised discriminant analysis
Dirichlet random values simulation

Dirichlet random values simulation
Non linear least squares regression for compositional data

Non linear least squares regression for compositional data
Principal components regression

Principal components regression
Spatial median regression

Spatial median regression
Tuning of the divergence based regression for compositional data with compositional data in the covariates side using the alpha-transformation

Tuning of the divergence based regression for compositional data with compositional data in the covariates side using the \(alpha\)-transformation
Log-likelihood ratio test for a symmetric Dirichlet distribution

Log-likelihood ratio test for a symmetric Dirichlet distribution
Multivariate analysis of variance

Multivariate analysis of variance
Power operation

Power operation
Quasi binomial regression for proportions

Quasi binomial regression for proportions
Simulation of compositional data from the folded model

Simulation of compositional data from the folded model
Ridge regression plot

Ridge regression plot
Regularised discriminant analysis for compositional data using the alpha-transformation

Regularised discriminant analysis for compositional data using the \(\alpha\)-transformation