Bayesian latent class analysis with sparse finite mixtures

Music City Center 

We propose the use of overfit mixture models to select the number of components for categorical data with multiple items in the response variable. Latent class analysis (LCA) requires the user to specify the number of classes in the population. Since this is often unknown to the researcher, many studies have investigated the performance of selection criteria, including hypothesis tests, likelihood-based information criteria, and cluster-based information criteria. Alternatively, for Gaussian mixtures, sparse finite mixtures allow a user to fit a model with a large number of components and learn the number of active components a posteriori. We adapt sparse finite mixtures to select the number of components for the LCA model. We provide careful recommendations for priors on the item response probabilities and component means to produce model selection for varying dimensions of the response variable.

Latent class analysis

Bayesian mixture model

Cluster analysis 

Section on Bayesian Statistical Science