title: Local influence diagnostics for hierarchical count data models with overdispersion and excess zeros.
abstract: We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs et al. () and Molenberghs et al. () 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 et al. (). 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.
authors.affiliation: I-BioStat, Universiteit Hasselt, Martelarenlaan 42, B-3500 Hasselt, Belgium. triaswahyuni.rakhmawati@uhasselt.be.
authors.forename: Trias Wahyuni
authors.initials: TW
authors.lastname: Rakhmawati
authors.affiliation: I-BioStat, Universiteit Hasselt, Martelarenlaan 42, B-3500 Hasselt, Belgium.|I-BioStat, KU Leuven, Kapucijnenvoer 35, B-3000 Leuven, Belgium.
authors.forename: Geert
authors.initials: G
authors.lastname: Molenberghs
authors.affiliation: I-BioStat, Universiteit Hasselt, Martelarenlaan 42, B-3500 Hasselt, Belgium.|I-BioStat, KU Leuven, Kapucijnenvoer 35, B-3000 Leuven, Belgium.
authors.forename: Geert
authors.initials: G
authors.lastname: Verbeke
authors.affiliation: I-BioStat, Universiteit Hasselt, Martelarenlaan 42, B-3500 Hasselt, Belgium.|I-BioStat, KU Leuven, Kapucijnenvoer 35, B-3000 Leuven, Belgium.
authors.forename: Christel
authors.initials: C
authors.lastname: Faes
mesh_terms: D001699:Biometry / Q000379:methods*; D004827:Epilepsy / Q000175:diagnosis; D006801:Humans; D016014:Linear Models; D008137:Longitudinal Studies; D016012:Poisson Distribution
keywords: Combined model; Excess zero; Hurdle model; Local influence; Overdispersion; Poisson-normal model; Zero-inflated model