Variational Bayesian analysis for two-part latent variable model

It is recommended to use two-part models for analyzing zero-inflated data that exhibit a spike at zero or have a large proportion of participants with zero values. This paper presents a variational Bayesian inference procedure for the analysis of a two-part latent variable model. We take advantage of the Pólya Gamma stochastic representation to approximate the posterior distribution via a mean-field variational method. We propose a scheme to update the variational parameters using the coordinate ascent inference algorithm and develop a variational Bayes based procedure for the variable selection and model assessment. We conduct simulation studies to assess the performance of our proposed method and compare it with the Markov Chains Monte Carlo sampling method. Our results show that the proposed variational Bayesian approach achieves computational efficiency without sacrificing estimation accuracy. We further illustrate the practical merits of the proposed approach by analyzing household finance survey data.