Simulation Studies for a Special Mixture Regression Model with Multivariate Responses on the Simplex

Compositional data are defined as vectors whose elements are strictly positive and subject to a unit sum constraint. When the multivariate response is of compositional type, a proper regression model that takes account of the unit-sum constraint is required. This chapter illustrates a new multivariate regression model for compositional data that is based on a mixture of Dirichlet-distributed components. It aims to intensively study the behavior of the Extended Flexible Dirichlet (EFD) regression model in many simulated scenarios covering some relevant statistical issues such as the presence of outliers, heavy tails and latent groups. The chapter also introduces the Dirichlet and the EFD distributions, and shows convenient parameterizations for regression purposes. It then outlines details on the EFD regression model and provides an overview on the Hamiltonian Monte Carlo algorithm, a Bayesian approach to inference especially suited for mixture models.