Dirichlet negative multinomial regression for overdispersed correlated count data

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A generic random effects formulation for the Dirichlet negative multinomial distribution is developed together with a convenient regression parameterization. A simulation study indicates that, even when somewhat misspecified, regression models based on the Dirichlet negative multinomial distribution have smaller median absolute error than generalized estimating equations, with a particularly pronounced improvement when correlation between observations in a cluster is high. Estimation of explanatory variable effects and sources of variation is illustrated for a study of clinical trial recruitment.

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