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Using Bayesian Priors for More Flexible Latent Class Analysis

Latent class analysis is based on the assumption that within each class the observed class indicator variables are independent of each other. We explore a new Bayesian approach that relaxes this assumption to an assumption of approximate independence. Instead of using a correlation matrix with correlations fixed to zero we use a correlation matrix where all correlations are estimated using an informative prior with mean zero but non-zero variance. This more flexible approach easily accommodates LCA model misspecifications and thus avoids spurious class formations that are caused by the conditional independence violations. Simulation studies and real data analysis are conducted using Mplus.