Space-Time Areal Mixture Model: Relabeling Algorithm and Model Selection Issues

With the growing popularity of spatial mixture models in cluster analysis, model selection criteria have become an established tool in the search for parsimony. However, the label-switching problem is often inherent in Bayesian implementation of mixture models and a variety of relabeling algorithms have been proposed. We use a space-time mixture of Poisson regression models with homogeneous covariate effects to illustrate that the best model selected by using model selection criteria does not always support the model that is chosen by the optimal relabeling algorithm. The results are illustrated for real and simulated datasets. The objective is to make the reader aware that if the purpose of statistical modeling is to identify clusters, applying a relabeling algorithm to the model with the best fit may not generate the optimal relabeling.