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

Abstract

Semi-continuous data are very common in the social science and economics. In this paper, a Bayesian variable selection procedure is developed to assess the influence of exogenous factors including observed and unobserved on the semi-continuous data. Our formulation is based on the two-part latent variable model with polytomous response. We consider two schemes for the penalties of regression coefficients and factor loadings: the Bayesian spike and slab bimodal prior and the Bayesian lasso prior. Within the Bayesian framework, we implement Markov Chains Monte Carlo sampling method to conduct posterior inference. To facilitate posterior sampling, we recast the logistic model in part one as the norm-like mixture model. Gibbs sampler is designed to draw observations from the posterior. Our empirical results show that with suitable hyper-parameters, the spike and slab bimodal method slightly outperforms the Bayesian lasso in the current analysis. Finally, a real example related to the China household finance survey is analyzed to illustrate the application of the methodology.. .