SGB-package {SGB}

Package SGB

Description

Package SGB contains a generalization of the Dirichlet distribution, called the Simplicial Generalized Beta (SGB). It is a new distribution on the simplex (i.e. on the space of compositions or positive vectors with sum of components equal to 1). The Dirichlet distribution can be constructed from a random vector of independent Gamma variables divided by their sum. The SGB follows the same construction with generalized Gamma instead of Gamma variables. The Dirichlet exponents are supplemented by an overall shape parameter and a vector of scales. The scale vector is itself a composition and can be modeled with auxiliary variables through a log-ratio transformation.

Details

Index of help topics:

B2i                     Balances to isometric log-ratio
EZ.SGB                  Expectations of Z under the SGB distribution
EqualityConstr          Equality constraints for overall shape and/or
                        regression parameters and jacobian
GenGammaDistrib         Generalized Gamma distribution
GoodnessFit             Goodness of fit tests on the marginal
                        distributions of each part in a SGB model
Imputation              Imputation of missing parts in compositions
                        from a SGB model
InequalityConstr        Inequality constraints and jacobian
InitialParameters       Initial parameters estimates and comparison
MarginPlots             Histograms, quantile and probability plots for
                        the z(u)-transforms of parts
SGB-package             Package SGB
SGBLik                  SGB log-likelihood and gradient
SGBdistrib              Density and random generator for the SGB
                        distribution
SGButil                 Computation of scales and z-vectors
Tabulation              Tabulation of overall SGB regression results
                        with AIC and matrix view of regression
                        coefficients
arc                     arc dataset
carseg                  carseg dataset
covest.SGB              Classical and robust asymptotic covariance
                        matrix
ocar                    ocar data set
oilr                    oilr data set
regSGB                  Regression for compositions following a SGB
                        distribution
stepSGB                 Stepwise backward elimination for SGB
                        regression
summaryA.SGB            Aitchison expectation and mode under the SGB
                        distribution

Further information is available in the following vignettes:

vignette	SGB multivariate regression (source, pdf)

Author(s)

Monique Graf

Maintainer: Monique Graf <[e-mail]>

References

Graf, M. (2017). A distribution on the simplex of the Generalized Beta type. In J. A. Martin-Fernandez (Ed.), Proceedings CoDaWork 2017, University of Girona (Spain), 71-90.

Graf, M. (2019). The Simplicial Generalized Beta distribution - R-package SGB and applications. Proceedings of the 8th International Workshop on Compositional Data Analysis (CoDaWork2019): Terrassa, 3-8 June, 2019. J.J. Egozcue, J. Graffelman and M.I. Ortego (Editors). Universitat Politecnica de Catalunya-BarcelonaTECH, 2019. 202 p. ISBN 978-84-947240-2-2. .

Graf, M. (2020). Regression for compositions based on a generalization of the Dirichlet distribution. Statistical Methods & Applications, (), 1-24.

Examples

## Result of a regression object:
summary(oilr)