BIC selection of the number of classes in latent class models with background variables

摘要

For selecting the number of classes in mixture models, including latent class models, the Bayesian Information Criterion (BIC) is widely used. In normal mixture models. BIC is known to suffer from the problem of underestimating the true number of classes in high dimensional data where background variables, irrelevant to the clustering, are present. However, this problem has received less attention in the context of latent class models. In the present paper, we study the behavior of BIC in latent class models. First, we derive an analytical approximation of the expectation of BIC. Using this result, we show that also in latent class models with background variables BIC suffers from underestimating the true number of classes. Second, we propose a solution to this problem in terms of a corrected BIC. Finally, we report the results of a limited simulation study, which gives a first indication that the corrected BIC may have a good performance with regard to model selection.