MODEL CHOICE - A MINIMUM POSTERIOR PREDICTIVE LOSS APPROACH

Model choice is a fundamental and much discussed activity in the analy sis of datasets. Nonnested hierarchical models introducing random effe cts may not be handled by classical methods. Bayesian approaches using predictive distributions can be used though the formal solution, whic h includes Bayes factors as a special case, can be criticised. We prop ose a predictive criterion where the goal is good prediction of a repl icate of the observed data but tempered by fidelity to the observed va lues. We obtain this criterion by minimising posterior loss for a give n model and then, for-models under consideration, selecting the one wh ich minimises this criterion. For a broad range of losses, the criteri on emerges as a form partitioned into a goodness-of-fit term and a pen alty term. We illustrate its performance with an application to a larg e dataset involving residential property transactions.