Estimation and Model Selection in Dirichlet Regression

We study Compositional Models based on Dirichlet Regression where, given a (vector) covariate x, one considers the response variable y = (y(1), ... , y(D)) to be a positive vector with a conditional Dirichlet distribution, y vertical bar x similar to D (alpha(1) (x) ... alpha(D)(x)). We introduce a new method for estimating the parameters of the Dirichlet Covariate Model when alpha(j)(x) is a linear model on x, and also propose a Bayesian model selection approach. We present some numerical results which suggest that our proposals are more stable and robust than traditional approaches.