Abstract:
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The latent class model, a type of finite mixture model, is frequently used in behavioral sciences to infer composition and structure of latent groups in a population that generates binary data. In practice, the number of latent classes is unknown and the need to estimate the number hampers the interpretability and reproducibility of results from these models. Model selection in latent class analysis is difficult because popular selection criteria such as AIC and BIC are sensitive to features of the data such as sample size and dimension of the response.
Recently, Bayesian approaches have been developed to use finite mixture models when the number of components is unknown. We investigate the operating characteristics of two such approaches, mixtures of finite mixtures and sparse finite mixtures, in data whose structure matches that of binary survey data sets often encountered in the behavioral sciences. Specifically, we develop hierarchical models that account for common features in these data, and we investigate the effect of non-informative and theoretically-motivated prior distributions on the inferred number of classes.
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