Applied Modeling Techniques and Data Analysis 2

12A Flexible Mixture Regression Model for Bounded Multivariate Responses

Compositional data are defined as vectors with strictly positive elements subject to a unit-sum constraint. The aim of this contribution is to propose 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. A convenient parameterization of the FD is provided which is variation independent and facilitates the interpretation of the mean vector of each mixture component as a piecewise increasing linear function of the overall mean vector. A multivariate logit strategy is adopted to regress the vector of means, which is itself constrained to add up to one, onto a vector of covariates. Intensive simulation studies are performed to evaluate the fit of the proposed regression model, particularly in comparison with the Dirichlet regression model. Inferential issues are dealt with by a (Bayesian) Hamiltonian Monte Carlo algorithm.

12.1. Introduction

Compositional data, namely proportions of some whole, are defined on the simplex space . Many fields of ...