Bayesian analysis for two-part latent variable model with application to fractional data

Abstract

Fractional data suffering from large proportion of values at boundaries are very common in the social and economic surveys. Existing literature usually separates the whole data into three parts and specifies a three-part regression model to them. In this article, we develop an attractive two-part latent variable model for fractional data. The separated three parts are synthesized into two parts to characterize the association among the whole data. Moveover, latent variables are incorporated into the data analysis to interpret extra heterogeneity and item-dependence. We also include a structural equation to explore the interrelationships among the multiple factors. To downweight the influence of the distributional deviations and/or outliers, we develop a semiparametric Bayesian analysis procedure. Parameter estimation and model assessment are obtained via Markov Chain Monte Carlo sampling method. A real example pertaining to the cocaine use is presented to illustrate the proposed methodology.