Bettina Grün (Institute of Applied Statistics, Johannes Kepler University Linz) about "Shrinkage Priors for Sparse Latent Class Analysis".

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Abstract:
Model-​based clustering aims at finding latent groups in multivariate data based on mixture models. In this context the latent class model is commonly used for multivariate categorical data. Important issues to address are the selection of the number of clusters as well as the identification of a suitable set of clustering variables. In a maximum likelihood estimation context Fop et al. (2017) propose a step-​wise procedure based on the BIC for model as well as variable selection for the latent class model. They explicitly distinguish between relevant, irrelevant and redundant variables and indicate that their approach leads to a parsimonious solution where the latent groups correspond to a known classification of the data.
In the Bayesian framework we propose a model specification based on shrinkage priors for the latent class model to obtain sparse solutions. In particular regarding variable selection we emphasize the distinction between the different roles of the variables made in the literature so far and the implications on prior choice. We outline the estimation based on Markov chain Monte Carlo methods and post-​processing strategies to identify the clustering solution. Advantages of the Bayesian approach are that the computational demanding step-​wise procedure is avoided, regularization is naturally imposed to eliminate degenerate solutions and the exploratory nature of clustering is supported by enabling an adaptive way to reveal competing clustering structures from coarser to more fine-​grained solutions.

Institute for Statistics and Mathematics