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Ignoring overdispersion in hierarchical loglinear models: Possible problems and solutions

Poisson data frequently exhibit overdispersion; and, for univariate models, many options exist to circumvent this problem. Nonetheless, in complex scenarios, for example, in longitudinal studies, accounting for overdispersion is a more challenging task. Recently, Molenberghs et.al, presented a model that accounts for overdispersion by combining two sets of random effects. However, introducing a new set of random effects implies additional distributional assumptions for intrinsically unobservable variables, which has not been considered before. Using the combined model as a framework, we explored the impact of ignoring overdispersion in complex longitudinal settings via simulations. Furthermore, we evaluated the effect of misspecifying the random‐effects distribution on both the combined model and the classical Poisson hierarchical model. Our results indicate that even though inferences may be affected by ignored overdispersion, the combined model is a promising tool in this scenario. Copyright © 2012 John Wiley & Sons, Ltd.