  We propose a Bayesian approach for model-based clustering of multivariate
categorical data where variables are allowed to be associated within clusters
and the number of clusters is unknown. The approach uses a two-layer mixture of
finite mixtures model where the cluster distributions are approximated using
latent class analysis models. A careful specification of priors with suitable
hyperparameter values is crucial to identify the two-layer structure and obtain
a parsimonious cluster solution. We outline the Bayesian estimation based on
Markov chain Monte Carlo sampling with the telescoping sampler and describe how
to obtain an identified clustering model by resolving the label switching
issue. Empirical demonstrations in a simulation study using artificial data as
well as a data set on low back pain indicate the good clustering performance of
the proposed approach, provided hyperparameters are selected which induce
sufficient shrinkage.
