Modeling Compositional Regression with uncorrelated and correlated errors: a Bayesian approach

Abstract

Compositional data consist of known compositions vectors whose components are positive and defined in the interval (0,1) representing proportions or fractions of a "whole". The sum of these components must be equal to one. Compositional data is present in different knowledge areas, as in geology, economy, medicine among many others. In this paper, we introduce a Bayesian analysis for compositional regression applying additive log-ratio (ALR) transformation and assuming uncorrelated and correlated errors. The Bayesian inference procedure based on Markov Chain Monte Carlo Methods (MCMC). The methodology is illustrated on an artificial and a real data set of volleyball.