Data Analysis and Related Applications, Volume 1

9Simulation 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 contribution illustrates a new multivariate regression model for compositional data that is based on a mixture of Dirichlet-distributed components. Its complex structure is offset by good theoretical properties (among which identifiability) and a greater flexibility than the standard Dirichlet regression model. We perform intensive simulation studies to evaluate the fit of the proposed regression model and its robustness in the presence of multivariate outliers. The (Bayesian) estimation procedure is performed via the efficient Hamiltonian Monte Carlo algorithm.

9.1. Introduction

Compositional data, namely proportions of some whole, are encountered in several fields of science and require proper statistical tools of analysis (Aitchison 2003). Indeed, compositional data have the peculiarity of being vector of proportions lying on the simplex space: . The analysis of compositional data is challenging since it cannot make use of standard techniques that might lead to distorted results due to ignoring the unit-sum constraint. ...