A Poisson Mixed Model with Nonnormal Random Effect Distribution

Details A Poisson Mixed Model with Nonnormal Random Effect Distribution A Poisson Mixed Model with Nonnormal Random Effect Distribution

2011-05-10

arxiv.org/abs/1105.2072v1

Statistics

Methodology

Submitted in the Computational Statistics & Data Analysis journal

Scientific paper

We propose in this paper a random intercept Poisson model in which the random effect distribution is assumed to follow a generalized log-gamma (GLG) distribution. 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 for 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 are proposed and two applications with real data are given for illustration.

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