Confirmatory Latent Class Analysis: Model Selection Using Bayes Factors and (Pseudo) Likelihood Ratio Statistics

Inequality constraints among class specific probabilities can be used to assign a specific meaning to the classes in a latent class model. Different models arise if different sets of constraints are used. In this paper, model selection using Bayes factors, and, (pseudo) likelihood ratio statistics evaluated using posterior predictive p-values, will be discussed. It will be illustrated that these Bayesian selection criteria do not suffer from the same flaw as maximum likelihood based selection criteria. Using a small simulation study it will be shown that, in the context of the simulation study, Bayes factors and the pseudo likelihood ratio statistic have the best proporties. The article will be concluded with an example.