On diagnostics in log-linear negative binomial models

Abstract

We discuss in this paper application of goodness-of-fit diagnostics in log-linear negative binomial models. This kind of model, that belongs to the class of hierarchical generalized linear models, has been applied for modeling the phenomenon of overdispersion under loglinear Poisson models. We derive the appropriate matrices for assessing the local influence on the parameter estimates that may affect the mean structure as well as the variance function of the negative binomial models. In addition, we perform a small simulation study in order to investigate the empirical distribution of the deviance residual. Two examples, for which we apply the goodness-of-fit diagnostic methods, are given as illustration.

Keywords:

• Count data
• Influence diagnostic
• Lack-of-fit
• Likelihood displacement
• Residual analysis
• Overdispersion
• Variance function