A Flexible Mixture Regression Model for Bounded Multivariate Responses

This chapter proposes a regression model for multivariate continuous variables with bounded support by taking into consideration the flexible Dirichlet (FD) distribution that can be interpreted as a special mixture of Dirichlet distributions. The FD distribution is an extension of the Dirichlet one, which is contained as an inner point, and it enables a greater variety of density shapes in terms of tail behavior, asymmetry and multimodality. The chapter describes the FD regression (FDReg) model for compositional data. It provides details on a Bayesian approach to inference suitable for the FDReg model. Inferential issues are dealt with by a (Bayesian) Hamiltonian Monte Carlo algorithm. The chapter illustrates several simulation studies that have been performed to evaluate the behavior of the proposed regression model.