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Multivariate models for correlated count data

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In this study, we deal with the problem of overdispersion beyond extra zeros for a collection of counts that can be correlated. Poisson, negative binomial, zero-inflated Poisson and zero-inflated negative binomial distributions have been considered. First, we propose a multivariate count model in which all counts follow the same distribution and are correlated. Then we extend this model in a sense that correlated counts may follow different distributions. To accommodate correlation among counts, we have considered correlated random effects for each individual in the mean structure, thus inducing dependency among common observations to an individual. The method is applied to real data to investigate variation in food resources use in a species of marsupial in a locality of the Brazilian Cerrado biome.
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Keywords: Poisson distribution; maximum likelihood; mixed model; mixture distribution; multivariate count data; negative binomial distribution; overdispersion; zero-inflated data

Document Type: Research Article

Affiliations: 1: Department of Statistics, University of Campinas, Campinas, 13083-859, Brazil 2: Department of Forest Sciences, Centre for Applied Conservation Research, University of British Columbia, Vancouver, Canada V6T1Z4, 3: Departamento de Ecologia, Universidade Estadual Paulista, Rio Claro, 13506-900, Brazil 4: Departamento de Biologia Animal, Universidade Estadual de Campinas, Campinas, 13083-862, Brazil

Publication date: July 1, 2013

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