Local influence diagnostics for hierarchical count data models with overdispersion and excess zeros

We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs etal. () and Molenberghs etal. () extend the Poisson-normal generalized linear-mixed model by including gamma random effects to accommodate overdispersion. Excess zeros are handled using either a zero-inflation or a hurdle component. These models were studied by Kassahun etal. (). While flexible, they are quite elaborate in parametric specification and therefore model assessment is imperative. We derive local influence measures to detect and examine influential subjects, that is subjects who have undue influence on either the fit of the model as a whole, or on specific important sub-vectors of the parameter vector. The latter include the fixed effects for the Poisson and for the excess-zeros components, the variance components for the normal random effects, and the parameters describing gamma random effects, included to accommodate overdispersion. Interpretable influence components are derived. The method is applied to data from a longitudinal clinical trial involving patients with epileptic seizures. Even though the data were extensively analyzed in earlier work, the insight gained from the proposed diagnostics, statistically and clinically, is considerable. Possibly, a small but important subgroup of patients has been identified.