Document details for 'Modelling count data using the logratio-normal-multinomial distribution'

Authors Comas-Cufi, M., Martin-Fernandez, J.A., Mateu-Figueras, G. and Palarea Albaladejo, J.
Publication details Statistics and Operations Research Transactions 44(1), 99-126. Statistical Institute of Catalonia, Barcelona, Spain.
Publisher details Statistical Institute of Catalonia, Barcelona, Spain
Keywords Count data, Compound probability distribution, Dirichlet Multinomial, Logratio coordinates, Monte Carlo method, Simplex
Abstract Compound probability distributions are useful for modelling and analysing multivariate count data. 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. This distribution stands out as a more flexible model for count data than the commonly used Dirichlet-multinomial distribution. 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 were 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 were compared through a number of examples using simulated and real count data. The latter model provided more realistic results, particularly when a complex variability structure in the vector of multinomial probabilities was considered.
Last updated 2020-06-29

Unless explicitly stated otherwise, all material is copyright © Biomathematics and Statistics Scotland.

Biomathematics and Statistics Scotland (BioSS) is formally part of The James Hutton Institute (JHI), a registered Scottish charity No. SC041796 and a company limited by guarantee No. SC374831. Registered Office: JHI, Invergowrie, Dundee, DD2 5DA, Scotland