Estimation of spatially correlated random scaling factors based on Markov random field priors

Multiplicative random effects allow for cluster-specific scaling of covariate effects. In many applications with spatial clustering, however, the random effects additionally show some geographical pattern, which usually can not sufficiently be captured with existing estimation techniques. Relying on Markov random fields, we present a fully Bayesian inference procedure for spatially correlated scaling factors. The estimation is based on highly efficient Markov Chain Monte Carlo (MCMC) algorithms and is smoothly incorporated into the framework of distributional regression. We run a comprehensive simulation study for different response distributions to examine the statistical properties of our approach. We also compare our results to those of a general estimation procedure for independent random scaling factors. Furthermore, we apply the method to German real estate data and show that exploiting the spatial correlation of the scaling factors further improves the performance of the model.