A Bayesian approach to the selection and testing of latent class models

An important part of a latent class analysis concerns the selection of the number of latent classes. In this paper, we discuss the Bayes factor as a selection tool. The discussion will focus on two aspects: (i) the computation of the Bayes factor and (ii) prior sensitivity. To deal with prior sensitivity, we propose to extend the model with a prior for the hyperparameters. We further discuss the use of posterior predictive checks for examining the fit of the model. The ideas are illustrated by means of a psychiatric diagnosis example.