Regression for compositions based on a generalization of the Dirichlet distribution

摘要

The simplex is the geometrical locus of D-dimensional positive data with constant sum, called compositions. A possible distribution for compositions is the Dirichlet. In Dirichlet models, there are no scale parameters and the D shapes are assumed dependent on auxiliary variables. This peculiar feature makes Dirichlet models difficult to apply and to interpret. Here, we propose a generalization of the Dirichlet, called the simplicial generalized Beta (SGB) distribution. It includes an overall shape parameter, a scale composition and the D Dirichlet shapes. The SGB is flexible enough to accommodate many practical situations. SGB regression models are applied to data from the United Kingdom Time Use Survey. The R-package SGB makes the methods accessible to users.