Title: Dealing with count zeros in compositional data analysis using the logratio-normal-multinomial distribution
Authors: Josep Antoni Martin-Fernandez - University of Girona (Spain)
Gloria Mateu-Figueras - University of Girona (Spain)
Javier Palarea-Albaladejo - Biomathematics and Statistics Scotland (United Kingdom)
Marc Comas-Cufi - Universitat de Girona (Spain) [presenting]
Abstract: Multivariate count data are commonly modelled using the multinomial distribution. The Dirichlet distribution has been proposed for the multinomial probability parameter to account for data overdispersion. In this scenario, the resulting compound distribution is the so-called Dirichlet-multinomial (DM) distribution. Although it satisfies appealing mathematical properties, the DM distribution assumes a fairly rigid covariance structure in practice. Alternatively, the logratio-normal-multinomial (LNM) distribution is the compound probability distribution resulting from considering a multivariate logistic-normal as the distribution for the probability parameter of the multinomial distribution. Compositional analysis of multivariate count data focuses on the logratios between multinomial components and, hence, the presence of zero counts is a practical problem. We introduce a new computational treatment of count zeros based on the LNM model. A quasi-Monte Carlo EM algorithm is implemented to estimate the model parameters. The performance of our proposal will be illustrated using real and simulated data sets and compared with existing approaches.