Bayesian-type count data models with varying coefficients: estimation and testing in the presence of overdispersion

In this paper we study varying-coefficient models for count data. A Bayesian approach is taken to model the variability of the regression parameters. Based on a Kalman filter procedure the varying coefficients are estimated as the mode of the posterior distribution. All hyperparameters, including an overdispersion parameter in the negative binomial varying-coefficient model (NBVC), are estimated as ML-estimators using an EM-type algorithm. A bootstrapping test of the fixed-coefficient hypothesis against a varying-coefficient alternative is proposed, which is evaluated running a simulation study. The study shows that the choice of a suitable count data model is of special importance in the framework of varying-coefficient models. The methodology is illustrated analysing the determinants of the number of individual doctor visits. Copyright (C) 2001 John Wiley & Sons, Ltd.