Semiparametric Bayesian Count Data Models

Abstract

Count data models have a large number of pratical applications. However there can be several problems which prevent the use of the standard Poisson regression. We may detect individual unobserved heterogeneity, caused by missing covariates, and/or excess of zero observations in our data. Both distributional issues results in deviations of the response distribution from the classical Poisson assumption. We may in addition want to extend our predictor to model temporal or spatial correlation and possibly nonlinear effects of continuous covariates or time scales available in the data. Here we study and develop semiparametric count data models which can solve these problems. We have extended the Poisson distribution to account for overdispersion and/or zero inflation. Additionally we have incorporated corresponding components in structured additive form into the predictor. The models are fully Bayesian and inference is carried out by computationally efficient MCMC techniques. In simulation studies, we investigate how well the different components can be identified with the data at hand. Finally, the approaches are applied to two data sets: to a patent data set and to a large data set of claim frequencies from car insurance.