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 areas, as in ecology, economy, medicine among many others .In this way, there is a great interest in new modeling approaches for compositional data. In this research project we will study existing additive log-ratio transformation models used for compositional data, under correlated and uncorrelated normal errors under different distributions in comparison with other existing modeling approaches introduced in the literature to deal with compositional data, as standard Dirichlet regression models which generalizes standard Beta regression models. The main objective of this project is to apply Bayesian methods to these models using standard Markov Chain Monte Carlo methods to simulate samples of the joint posterior of interest. In the selection of models that best fit the real or simulated data sets, we will explore some Bayesian discrimination methods as the Bayes Factor or DIC (Deviance Information Criteria). Some other important points also will be studied: missing data, effect of different priors, reparametrizations to improve the convergence of the simulation algorithms.These new modeling results could be of great interest in the applied work dealing with compositional data sets.
News published in Agência FAPESP Newsletter about the scholarship: