Bayesian‐type count data models with varying coefficients: estimation and testing in the presence of overdispersion
Ludwig Fahrmeir, Jochen Mayer · Applied Stochastic Models in Business and Industry · 2001
Abstract 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 © 2001 John Wiley & Sons, Ltd.