Evaluating information criteria in latent class analysis: application to identify classes of breast cancer dataset

In recent studies, latent class analysis (LCA) modelling has been proposed as a convenient alternative to standard classification methods. It has become a popular tool for clustering respondents into homogeneous subgroups based on their responses on a set of categorical variables. The absence of a common accepted statistical indicator for deciding the number of classes in the study of population represents one of the major unresolved issues in the application of the LCA. Determining the number of classes constituting the profiles of a given population is often done by using the likelihood ratio test, however the use of such methodology is not correct theoretically. To overcome this problem, we propose an alternative for the classical latent class models selection methods based on the information criteria. This article aims to investigate the performance of information criteria for selecting the latent class analysis models. Nine information criteria are compared under various sample sizes and model dimensionality. We propose also an application of ICs to select the best model of breast cancer dataset.