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Compositional (version 4.3)

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). A novel, divergence based, regression for compositional data. Proceedings of the 28th Panhellenic Statistics Conference, 15-18 April 2015, Athens, Greece, 430--444. d) Tsagris M. (2015). Regression analysis with compositional data containing zero values. Chilean Journal of Statistics, 6(2):47--57. e) 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. . f) 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. g) Tsagris M. and Stewart C. (2018). A Dirichlet regression model for compositional data with zeros. Lobachevskii Journal of Mathematics, 39(3): 398--412. . h) Alenazi A. (2019). Regression for compositional data with compositional data as predictor variables with or without zero values. Journal of Data Science, 17(1): 219--238. . i) Tsagris M. and Stewart C. (2020). A folded model for compositional data analysis. Australian and New Zealand Journal of Statistics, 62(2):249--277. . j) Tsagris M., Alenazi A. and Stewart C. (2020). The alpha-k-NN regression for compositional data. . We further include functions for percentages (or proportions).

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Version

Install

install.packages('Compositional')

Monthly Downloads

1,440

Version

4.3

License

GPL (>= 2)

Maintainer

Michail Tsagris

Last Published

January 19th, 2021

Functions in Compositional (4.3)

The alpha-k-NN regression for compositional response data

The \(\alpha\)-k-NN regression for compositional response data
Alpha generalised correlations between two compositional datasets

Alpha generalised correlations between two compositional datasets
The alpha-transformation

The \(\alpha\)-transformation
Compositional-package

Compositional Data Analysis
Cross validation for the alpha-k-NN regression for compositional response data

Cross validation for the \(\alpha\)-k-NN regression for compositional response data
The alpha-k-NN regression with compositional predictor variables

The \(\alpha\)-k-NN regression with compositional predictor variables
Tuning of the alpha generalised correlations between two compositional datasets

Tuning of the alpha generalised correlations between two compositional datasets
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
Estimation of the value of alpha via the profile log-likelihood

Estimation of the value of \(\alpha\) via the alfa profile log-likelihood
Estimation of the value of alpha in the folded model

Estimation of the value of \(\alpha\) in the folded model
The alpha-distance

The \(\alpha\)-distance
Cross validation for the regularised and flexible discriminant analysis with compositional data using the alpha-transformation

Cross validation for the regularised and flexible discriminant analysis with compositional data using the \(\alpha\)-transformation
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
Regression with compositional data using the alpha-transformation

Regression with compositional data using the \(\alpha\)-transformation
Fast estimation of the value of alpha

Fast estimation of the value of \(\alpha\)
Regularised and flexible discriminant analysis for compositional data using the alpha-transformation

Regularised and flexible discriminant analysis for compositional data using the \(\alpha\)-transformation
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
Tuning the value of alpha in the alpha-regression

Tuning the value of \(\alpha\) in the \(\alpha\)-regression
Ridge regression with the alpha-transformation plot

Ridge regression plot
MLE of the folded model for a given value of alpha

MLE of the folded model for a given value of \(\alpha\)
Beta regression

Beta regression
Cross validation for the alpha-k-NN regression with compositional predictor variables

Cross validation for the \(\alpha\)-k-NN regression with compositional predictor variables
MLE of distributions defined in the (0, 1) interval

MLE of distributions defined in the (0, 1) interval
Inverse of the alpha-transformation

Inverse of the \(\alpha\)-transformation
Contour plot of the t distribution in S^2

Contour plot of the t distribution in \(S^2\)
The k-nearest neighbours using the alpha-distance

The k-nearest neighbours using the \(alpha\)-distance
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
Projection pursuit regression for compositional data

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

Hypothesis testing for two or more compositional mean vectors
Mixture model selection via BIC

Mixture model selection via BIC
The additive log-ratio transformation and its inverse

The additive log-ratio transformation and its inverse
Estimating location and scatter parameters for compositional data

Estimating location and scatter parameters for compositional data
Multivariate regression with compositional data

Multivariate regression with compositional data
All pairwise additive log-ratio transformations

All pairwise additive log-ratio transformations
Tuning of the k-NN algorithm for compositional data

Tuning of the k-NN algorithm for compositional data
Density of the Dirichlet distribution

Density of the Dirichlet distribution
Dirichlet regression

Dirichlet regression
The ESOV-distance

The ESOV-distance
Contour plot of a Flexible Dirichlet distribution in S^2

Contour plot of a Flexible Dirichlet distribution in \(S^2\)
Density of the Flexible Dirichlet distribution

Density of the Flexible Dirichlet distribution
Choose the number of principal components via reconstruction error

Choose the number of principal components via reconstruction error
Log-likelihood ratio test for a Dirichlet mean vector

Log-likelihood ratio test for a Dirichlet mean vector
Fitting a Dirichlet distribution

Fitting a Dirichlet distribution
Divergence matrix of compositional data

Divergence matrix of compositional data
The Helmert sub-matrix

The Helmert sub-matrix
Fitting a Flexible Dirichlet distribution

Fitting a Flexible Dirichlet distribution
Fitting a Dirichlet distribution via Newton-Rapshon

Fitting a Dirichlet distribution via Newton-Rapshon
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
Generate random folds for cross-validation

Generate random folds for cross-validation
Cross validation for some compositional regression models

Cross validation for some compositional regression models
Helper Frechet mean for compositional data

Helper Frechet mean for compositional data
Tuning of the projection pursuit regression for compositional data

Tuning of the projection pursuit regression for compositional data
Power operation

Power operation
Estimation of the probability left outside the simplex when using the alpha-transformation

Estimation of the probability left outside the simplex when using the alpha-transformation
The Frechet mean for compositional data

The Frechet mean for compositional data
Contour plot of the folded model in S^2

Contour plot of the folded model in \(S^2\)
Multivariate analysis of variance

Multivariate analysis of variance
Multivariate analysis of variance (James test)

Multivariate analysis of variance (James test)
Contour plot of a Gaussian mixture model in S^2

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

Contour plot of a Dirichlet distribution in \(S^2\)
Contour plot of a Kent distribution in S^2

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

Kullback-Leibler divergence and Bhattacharyya distance between two Dirichlet distributions
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
Contour plot of the kernel density estimate in S^2

Contour plot of the kernel density estimate in \(S^2\)
Gaussian mixture models for compositional data

Gaussian mixture models for compositional data
Cross-validation for the constrained linear least squares for compositional responses and predictors

Cross-validation for the constrained linear least squares for compositional responses and predictors
The k-NN algorithm for compositional data

The k-NN algorithm for compositional data
Distance based regression models for proportions

Distance based regression models for proportions
MLE for the multivarite t distribution

MLE for the multivarite t distribution
Contour plot of the normal distribution in S^2

Contour plot of the normal distribution in \(S^2\)
Cross validation for the ridge regression

Cross validation for the ridge regression
Principal component generalised linear models

Principal component generalised linear models
Cross validation for the transformation-free linear regression for compositional responses and predictors

Cross validation for the transformation-free linear regression for compositional responses and predictors
Multivariate kernel density estimation

Multivariate kernel density estimation
Dirichlet random values simulation

Dirichlet random values simulation
Simulation of compositional data from the Flexible Dirichlet distribution

Simulation of compositional data from the Flexible Dirichlet distribution
Divergence based regression for compositional data

Divergence based regression for compositional data
Ridge regression

Ridge regression
Ridge regression plot

Ridge regression plot
Density values of a Dirichlet distribution

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

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

Empirical likelihood hypothesis testing for two mean vectors
Zero adjusted Dirichlet regression

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

Multivariate normal random values simulation on the simplex
Quasi binomial regression for proportions

Quasi binomial regression for proportions
Spatial median regression

Spatial median regression
Unit-Weibull regression models for proportions

Unit-Weibull regression models for proportions
Log-likelihood ratio test for a symmetric Dirichlet distribution

Log-likelihood ratio test for a symmetric Dirichlet distribution
Perturbation operation

Perturbation operation
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
Simulation of compositional data from the folded normal distribution

Simulation of compositional data from the folded model normal distribution
James multivariate version of the t-test

James multivariate version of the t-test
Ternary diagram

Ternary diagram
Ternary diagram of regression models

Ternary diagram of regression models
Regularised discriminant analysis for Euclidean data

Regularised discriminant analysis for Euclidean data
Constrained linear least squares for compositional responses and predictors

Constrained linear least squares for compositional responses and predictors
Transformation-free linear regression for compositional responses and predictors

Transformation-free linear regression for compositional responses and predictors
Non linear least squares regression for compositional data

Non linear least squares regression for compositional data
Tuning the principal components with GLMs

Tuning the principal components with GLMs
Aithison's simple zero replacement strategy

Aithison's simple zero replacement strategy
Total variability

Total variability
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
Greenacre's power transformation

Greenacre's power transformation
Tuning the parameters of the regularised discriminant analysis

Tuning the parameters of the regularised discriminant analysis
Helper functions for the Kullback-Leibler regression

Helper functions for the Kullback-Leibler regression
Multivariate t random values simulation on the simplex

Multivariate t random values simulation on the simplex
Multivariate linear regression

Multivariate linear regression
Simulation of compositional data from Gaussian mixture models

Simulation of compositional data from Gaussian mixture models
Multivariate skew normal random values simulation on the simplex

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

Contour plot of the skew skew-normal distribution in \(S^2\)