Latent class model diagnosis

In many areas of medical research, such as psychiatry and gerontology, latent class variables are used to classify individuals into disease categories, often with the intention of hierarchical modeling. Problems arise when it is not clear how many disease classes are appropriate, creating a need for model selection and diagnostic techniques. Previous work has shown that the Pearson χ² statistic and the log-likelihood ratio G² statistic are not valid test statistics for evaluating latent class models. Other methods, such as information criteria, provide decision rules without providing explicit information about where discrepancies occur between a model and the data. Identifiability issues further complicate these problems. This paper develops procedures for assessing Markov chain Monte Carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using Markov chain Monte Carlo techniques. Simulations and a psychiatric example are presented to demonstrate the effective use of these methods.