Bayesian Analysis of Two-Part Latent Variable Model with Mixed Data

In analyzing semi-continuous data, two-part model is a widely appreciated tool, in which two components are enclosed to characterize the mixing proportion of zeros and the actual level of positive values in semi-continuous data. The primary interest underlying such a model is primarily to exploit the dependence of the observed covariates on the semi-continuous variables; as such, the exploitation of unobserved heterogeneity is sometimes ignored. In this paper, we extend the conventional two-part regression model to much more general situations where multiple latent factors are considered to interpret the latent heterogeneity arising from the absence of covariates. A structural equation is constructed to describe the interrelationships between the latent factors. Moreover, a general statistical analysis procedure is developed to accommodate semi-continuous, ordered and unordered data simultaneously. A procedure for parameter estimation and model assessment is developed under a Bayesian framework. Empirical results including a simulation study and a real example are presented to illustrate the proposed methodology.