Fahrmeir, Ludwig; Lang, S.
Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data.
Collaborative Research Center 386, Discussion Paper 202
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. We provide two approaches: The first one is based on direct evaluation of observation likelihoods. The second one 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.