Modelling count data with overdispersion and spatial effects

In this paper we consider regression models for count data allowing
for overdispersion in a Bayesian framework. Besides the inclusion
of covariates, spatial effects are incorporated and modelled using
a proper Gaussian conditional autoregressive prior based on Pettitt
et al. (2002). Apart from the Poisson regression model, the
negative binomial and the generalized Poisson regression model are
addressed. Further, zero-inflated models combined with the Poisson
and generalized Poisson distribution are discussed.In an
application to a data set from a German car insurance company we
use the presented models to analyse the expected number of claims.
Models are compared according to the deviance information criterion
(DIC) suggested by Spiegelhalter et al. (2002). To assess the model
fit we use posterior predictive p-values proposed by Gelman et al.
(1996). For this data set no significant spatial effects are
observed, however the models allowing for overdispersion perform
better than a simple Poisson regression model.