Incorporating Marginal Prior Information in Latent Class Models

Abstract

We present an approach to incorporating informative prior beliefs about marginal probabilities into Bayesian latent class models for categorical data. The basic idea is to append synthetic observations to the original data such that (i) the empirical distributions of the desired margins match those of the prior beliefs, and (ii) the values of the remaining variables are left missing. The degree of prior uncertainty is controlled by the number of augmented records. Posterior inferences can be obtained via typical MCMC algorithms for latent class models, tailored to deal efficiently with the missing values in the concatenated data. We illustrate the approach using a variety of simulations based on data from the American Community Survey, including an example of how augmented records can be used to fit latent class models to data from stratified samples.