Alternative parameterizations for regression models with constrained multivariate responses

The extended flexible Dirichlet regression model has been recently proposed as a tool for modeling multivariate constrained responses. Being a special finite mixture, it displays a far richer dependence structure and a wider variety of shapes than the Dirichlet regression model. Moreover, it defines several group regression curves - one for each mixture component - which improve interpretation issues. Nonetheless, these curves may display non-smooth shapes which real datasets generally do not show. For this reason, we propose two alternative parameterizations able to fix this aspect, and we compare them both from an analytic and from a simulative point of view.