Modelling count data using the logratio-normal-multinomial distribution
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Marc Comas-Cufí [1] ; Josep Antoni Martín-Fernández [1] ; Glòria Mateu-Figueras [1] ; Javier Palarea-Albaladejo [1]
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[1] Universitat de Girona
Universitat de Girona
Gerona, España
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- Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 44, Nº. 1, 2020, págs. 99-126
- Idioma: inglés
- Enlaces
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Resumen
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.
