BAYESIAN SEMIPARAMETRIC REGRESSION ANALYSIS OF MULTICATEGORICAL TIME-SPACE DATA

LUDWIG FAHRMEIR AND STEFAN LANG

Department of Statistics, University of Munich, Ludwigstrasse 33, D-80539 Munich, Germany

(Received April 17, 2000; revised August 15, 2000)

Abstract. We present a unified semiparametric Bayesian approach based on Markov random field priors for analyzing the dependence of multicategorical response variables on time, space and further covariates. The general model extends dynamic, or state space, models for categorical time series and longitudinal data by including spatial effects as well as nonlinear effects of metrical covariates in flexible semiparametric form. Trend and seasonal components, different types of covariates and spatial effects are all treated within the same general framework by assigning appropriate priors with different forms and degrees of smoothness. Inference is fully Bayesian and uses MCMC techniques for posterior analysis. The approach in this paper is based on latent semiparametric utility models and is particularly useful for probit models. The methods are illustrated by applications to unemployment data and a forest damage survey.

Key words and phrases: Categorical time-space data, forest damage, latent utility models, Markov random fields, MCMC, probit models, semiparametric Bayesian inference, unemployment.