Modelling count data using the logratio-normal-multinomial distribution

Abstract

The logratio-normal-multinomial distribution is a count data model resulting from compounding a multinomial distribution for the counts with a multivariate logratio-normal distribution for the multinomial event probabilities. However, the logratio-normal-multinomial probability mass function does not admit a closed form expression and, consequently, numerical approximation is required for parameter estimation. In this work, different estimation approaches are introduced and evaluated. We concluded that estimation based on a quasi-Monte Carlo Expectation-Maximisation algorithm provides the best overall results. Building on this, the performances of the Dirichlet-multinomial and logratio-normal-multinomial models are compared through a number of examples using simulated and real count data.