Structured additive regression for overdispersed and zero‐inflated count data

In count data regression there can be several problems that prevent the use of the standard Poisson log‐linear model: overdispersion, caused by unobserved heterogeneity or correlation, excess of zeros, non‐linear effects of continuous covariates or of time scales, and spatial effects. We develop Bayesian count data models that can deal with these issues simultaneously and within a unified inferential approach. Models for overdispersed or zero‐inflated data are combined with semiparametrically structured additive predictors, resulting in a rich class of count data regression models. Inference is fully Bayesian and is carried out by computationally efficient MCMC techniques. Simulation studies investigate performance, in particular how well different model components can be identified. Applications to patent data and to data from a car insurance illustrate the potential and, to some extent, limitations of our approach. Copyright © 2006 John Wiley & Sons, Ltd.