A new regression model for bounded multivariate responses

The aim of this work is to propose a new multivariate regression model for compositional data, i.e., vectors of proportions. It is based on a mixture of Dirichletdistributed components and it enables many relevant properties for compositional data as well as accounting for positive correlations. Despite the complexity of the model, its special mixture structure provides a greater flexibility and a richer parameterization than the standard Dirichlet regression (DirReg) model and, moreover, guarantees its identifiability. We illustrate the performance and the goodness of fit of our new model through an application to the last Italian elections data.