Isaac Scientific Publishing

Journal of Advanced Statistics

Bayesian Inference on Bivariate Semi-continuous Mixed-effects Models with Application to Longitudinal Substance Use Data

Download PDF (674.5 KB) PP. 122 - 135 Pub. Date: September 1, 2016

DOI: 10.22606/jas.2016.13002


  • Dongyuan Xing
    College of Public Health, University of South Florida, Tampa, Florida, United States
  • Yangxin Huang*
    College of Public Health, University of South Florida, Tampa, Florida, United States
  • Henian Chen
    College of Public Health, University of South Florida, Tampa, Florida, United States
  • Yiliang Zhu
    College of Public Health, University of South Florida, Tampa, Florida, United States
  • Getachew A. Dagne
    College of Public Health, University of South Florida, Tampa, Florida, United States
  • Julie Baldwin
    College of Public Health, University of South Florida, Tampa, Florida, United States


Multivariate (bivariate) correlated data encountered frequently in longitudinal studies are often analyzed using a multivariate linear mixed-effects model with normality assumption. Semi-continuous data in the form of a mixture of high proportion of zeros and right-skewed positive values bring special challenges to the field of multivariate modeling. In this paper, we propose a Bayesian approach to analyze bivariate semi-continuous outcomes by jointly modeling a generalized logistic mixed-effects model on zero-inflation in either response and a bivariate linear mixed-effects model (BLMM) on the positive values given both responses occurred through a correlated randomeffects structure. Multivariate skew distributions including skew-t and skew-normal distributions are used to relax the normality assumption in BLMM. The proposed models are illustrated with an application to the correlated alcohol and drug uses data from a longitudinal observational study. A simulation study is conducted to evaluate the performance of the proposed models.


Bayesian analysis, Semi-continuous data, Joint modeling, Bivariate mixed-effects model, Skew distributions.


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