  Latent Class Models (LCMs) are used to cluster multivariate categorical data
(e.g. group participants based on survey responses). Traditional LCMs assume a
property called conditional independence. This assumption can be restrictive,
leading to model misspecification and overparameterization. To combat this
problem, we developed a novel Bayesian model called a Dependent Latent Class
Model (DLCM), which permits conditional dependence. We verify identifiability
of DLCMs. We also demonstrate the effectiveness of DLCMs in both simulations
and real-world applications. Compared to traditional LCMs, DLCMs are effective
in applications with time series, overlapping items, and structural zeroes.
