Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations

Qi Zhang, Yihui Zhang and Yemao Xia ()
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Qi Zhang: School of Science, Nanjing Forestry University, Nanjing 210037, China
Yihui Zhang: School of Computer Science, China University of Geosciences, Wuhan 430074, China
Yemao Xia: School of Science, Nanjing Forestry University, Nanjing 210037, China

Mathematics, 2024, vol. 12, issue 5, 1-23

Abstract: Semi-continuous data are very common in social sciences and economics. In this paper, a Bayesian variable selection procedure is developed to assess the influence of observed and/or unobserved exogenous factors on semi-continuous data. Our formulation is based on a two-part latent variable model with polytomous responses. We consider two schemes for the penalties of regression coefficients and factor loadings: a Bayesian spike and slab bimodal prior and a Bayesian lasso prior. Within the Bayesian framework, we implement a Markov chain Monte Carlo sampling method to conduct posterior inference. To facilitate posterior sampling, we recast the logistic model from Part One as a norm-type mixture model. A Gibbs sampler is designed to draw observations from the posterior. Our empirical results show that with suitable values of hyperparameters, the spike and slab bimodal method slightly outperforms Bayesian lasso in the current analysis. Finally, a real example related to the Chinese Household Financial Survey is analyzed to illustrate application of the methodology.

Keywords: two-part latent variable model; spike and slab prior; Bayesian lasso; MCMC sampling; CHFS (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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