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Abstract:
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In scientific problems where a vector of discrete responses is observed along with covariates, classical latent class regression models (LCRM) play a key role in studying their associations. In this paper, we propose a flexible Bayesian LCRM to 1) predict individual class labels, 2) perform non-constant selection for the weight curves, and 3) approximate the observed multivariate dependence with parsimony. Given covariates, our approach first decomposes a probability contingency table into classes, each characterized by a vector of response probabilities. We then mix these classes with weights that can depend on the covariates. We specify a sparsity prior that encourages mixing weights that are covariate-independent. We extend the decomposition to infinitely many classes and introduce a novel stick-breaking type prior on the class weights. The posterior distribution for the number of classes in the population is estimated from data and by design tends to concentrate on the smaller values. We demonstrate the method on both simulated data and real data from a multi-country childhood pneumonia etiology study.
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