A0341
Title: Modeling count compositions through a structured mixture of Dirichlet-multinomial components
Authors: Roberto Ascari - University of Milano-Bicocca (Italy) [presenting]
Abstract: Count compositions, or vectors of non-negative integers summing to a fixed total, are typically modeled using the multinomial distribution. While widely used, the multinomial has some limitations, particularly in its ability to capture positive covariance structures. One strategy to address this involves compounding the multinomial with a distribution defined on the simplex. A well-known example is the Dirichlet-multinomial (DM), which adds a parameter and improves the fit to real-world data, though it still imposes quite strong constraints on the covariance matrix. A novel distribution is introduced for count compositions, derived by compounding the multinomial with the extended flexible Dirichlet distribution. The resulting model can be seen as a structured finite mixture of specific DM components, allowing for greater flexibility and interpretability through latent group structures. Interestingly, it also allows for positive covariances. A regression model is developed based on this distribution, and its performance is evaluated through simulations and a real data application. Inference is conducted using a Bayesian framework, implemented via the Hamiltonian Monte Carlo algorithm.
