A New Regression Model for Count Compositions

Count compositions are vectors of non-negative integers summing to a fixed constant. This chapter briefly recalls the main results regarding two of the most popular distributions for count vectors, namely the multinomial and the Dirichlet-multinomial (DM). It proposes a new distribution for count compositions and develops a regression model based on it. The new distribution, flexible Dirichlet-multinomial is obtained by compounding the multinomial with the flexible Dirichlet, and it can be expressed as a structured finite mixture with particular DM components. The regression models are compared based on these new distributions through a simulation study and an application to a real dataset. Inferential issues are dealt with by a Bayesian approach through the Hamiltonian Monte Carlo algorithm. The chapter presents an application based on a real dataset concerning the results of the Italian general elections held in 2018.