Title: Variable selection in Bayesian latent class analysis using shrinkage priors
Authors: Gertraud Malsiner-Walli - WU Vienna University of Business and Economics (Austria) [presenting]
Bettina Gruen - Johannes Kepler University Linz (Austria)
Abstract: Latent class analysis uses mixture models to model multivariate categorical data where dependencies between variables are observed due to the presence of latent groups. Each latent group corresponds to a component in the mixture model and the variable distributions are independent within components. Applications of the latent class model are widespread within fields where categorical data are frequently collected such as medicine or the social sciences. Crucial issues in performing latent class analysis are to select a suitable number of filled components and the variables which are most informative for distinguishing between the components. Within a Bayesian context we propose an approach which addresses these two issues simultaneously. We specify suitable shrinkage priors for the component weights as well as the component-specific success probabilities. They induce sparsity with respect to the number of filled components as well as heterogeneity of the success probabilities across components. Standard estimation methods for Bayesian mixture models can be employed since the only difference to a standard Bayesian latent class analysis lies in the specification of suitable hierarchical priors with appropriate hyperparameter values. The application of this approach is investigated using simulation studies as well as real data.