Bayesian Semiparametric Regression Analysis of Multicategorical Time-Space Data

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.