Inference on Two-Part Latent Variable Analysis Model With Multivariate Longitudinal Data

Abstract

Semicontinuous variable analysis is a widely appreciated statistical method in such disciplines as social science, medicines, and economics. In detecting underlying structure and representing possible interrelationships, statistical analysis using a two-part model is appropriated. In this paper, we present a general extension of two-part model to the situation where the unobserved factors are included in the two parts to interpret external variability in semicontinuous variable. Auxiliary information on these factors is manifested by continuous responses via measurement model, while the interrelationships among factors are exploited through structural equation model. Moreover, under longitudinal setting, dynamic characteristics of responses between any two occasions are represented by transition model. Procedures for model fitting, parameter estimation, model selection and prediction are developed within the Bayesian paradigm. Markov Chains Monte Carlo method is used to implement posterior analysis. Empirical results including a simulation and a real example are used to illustrate the proposed methodology.

Keywords:

• Two-part latent variable model
• MCMC
• Gibbs sampler
• model comparison

ACKNOWLEDGMENT

The authors are grateful to the editor, the associate editor, and the three referees for their valuable suggestions and comments that have greatly improved the manuscript. The authors would be grateful to Prof. Xin-Yuan Song, Department of Statistics, Chinese University of Hong Kong, for using her cocaine use data.

Additional information

Funding

Xia’s work was supported by National Nature Science Foundation [NNSF 11471161, 11671349] and Natural Science Foundation of the Higher Education Institutions of Jiangsu Province [15KJB110010], and Tang’s work was supported by the Key Projects of National Nature Science Foundation [No.11731101] from China.