Title: Capturing correlated clusters using mixtures of latent class models
Authors: Gertraud Malsiner-Walli - WU Vienna University of Economics and Business (Austria) [presenting]
Abstract: Latent class models are useful for model-based clustering of multivariate categorical data. These models rely on the conditional independence assumption, i.e., it is assumed that the categorical variables are independent given the cluster membership. In case this assumption is violated, the latent class model will lead to more components being fitted than there are clusters in the data, as each cluster distribution will be approximated by several components. A crucial issue is then the identification of the clusters from the components as the likelihood is completely invariant to the assignment of components to a cluster. Within a Bayesian framework, we propose a suitable specification of priors for the latent class model to identify the clusters in multivariate categorical data where the independence assumption is not fulfilled. Each cluster distribution is approximated by a latent class model, leading overall to a mixture of latent class models. The Bayesian approach allows to identify the clusters and fits their cluster distributions using a one-step procedure, thus not relying on two-step procedures usually pursued in frequentist analysis where first a semi-parametric approximation using a latent class model with many components is performed and then components are combined to form clusters. We provide suitable estimation and inference methods for the mixture of latent class models and illustrate the performance of this approach on artificial and real data.