A Poisson mixed model with nonnormal random effect distribution

Lizandra C. Fabio, Gilberto A. Paula and Mário de Castro

Computational Statistics & Data Analysis, 2012, vol. 56, issue 6, 1499-1510

Abstract: In this paper, we propose a random intercept Poisson model in which the random effect is assumed to follow a generalized log-gamma (GLG) distribution. This random effect accommodates (or captures) the overdispersion in the counts and induces within-cluster correlation. We derive the first two moments for the marginal distribution as well as the intraclass correlation. Even though numerical integration methods are, in general, required for deriving the marginal models, we obtain the multivariate negative binomial model from a particular parameter setting of the hierarchical model. An iterative process is derived for obtaining the maximum likelihood estimates for the parameters in the multivariate negative binomial model. Residual analysis is proposed and two applications with real data are given for illustration.

Keywords: Count data; Generalized log-gamma distribution; Multivariate negative binomial distribution; Overdispersion; Random-effect models (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:6:p:1499-1510

DOI: 10.1016/j.csda.2011.12.002

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