Speaker
Description
Latent class models rely on the conditional
independence assumption, i.e., it is assumed that the categorical
variables are independent given the cluster memberships.
Within the 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 fit their
cluster distributions using a one-step procedure. 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.
Keywords: Bayesian inference, model-based clustering, prior on the number of components, telescoping sampler.
Fop, M., K. M. Smart, and T. B. Murphy (2017). Variable selection for latent
class analysis with application to low back pain diagnosis. The Annals of
Applied Statistics 11 (4), 2080-2110.
Fruehwirth-Schnatter, S., G. Malsiner-Walli, and B. Gruen (2021). Generalized
mixtures of finite mixtures and telescoping sampling. Bayesian
Analysis 16 (4), 1279–1307.
Malsiner-Walli, G., S. Fruehwirth-Schnatter, and B. Gruen (2017). Identifying
mixtures of mixtures using Bayesian estimation. Journal of Computational
and Graphical Statistics 26 (2), 285–295.
