Multivariate models for correlated count data |
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Authors: | Mariana Rodrigues-Motta Hildete P Pinheiro Eduardo G Martins Márcio S Araújo Sérgio F dos Reis |
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Institution: | 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. Department of Biology , Institute of Environmental Science, Carleton University , Ottawa , Canada , K1S5B6;4. Departamento de Ecologia , Universidade Estadual Paulista , Rio Claro , 13506-900 , Brazil;5. Departamento de Biologia Animal , Universidade Estadual de Campinas , Campinas , 13083-862 , Brazil |
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Abstract: | 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: | maximum likelihood mixed model mixture distribution multivariate count data overdispersion Poisson distribution negative binomial distribution zero-inflated data |
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