Statistics and Its Interface

Volume 10 (2017)

Number 4

Simultaneous Bayesian inference on a finite mixture of mixed-effects Tobit joint models for longitudinal data with multiple features

Pages: 557 – 573



Yangxin Huang (Department of Epidemiology and Biostatistics, Univ. of South Florida, Tampa, Fl., U.S.A.; Department of Statistics, Wuhan Univ. of Technology, Wuhan, Hubei, China; Department of Mathematics, Wuhan Textile Univ., Wuhan, China)

Jiaqing Chen (Department of Statistics, Wuhan University of Technology, Wuhan, Hubei, China)

Ping Yin (Department of Epidemiology and Biostatistics, Huazhong University of Science and Technology, Wuhan, Hubei, China)

Huahai Qiu (Department of Mathematics, Wuhan Textile University, Wuhan, China)


It often happens in longitudinal studies that some collected data are observed with the following issues. (i) Subjects may not sampled from homogeneous population with a common trajectory; (ii) longitudinal continuous measurements may suffer from a serious departure of normality in which normality assumption may cause lack of robustness and subsequently lead to invalid inference; (iii) some covariates of interest may be difficult to measure accurately due to their nature; and (iv) the response observations may be subject to left-censoring due to a limit of detection (LOD). Inferential procedures will become very complicated when one analyzes data with these features together. In the literature, there has been considerable interest in accommodating heterogeneity, non-normality, LOD or covariate measurement errors in longitudinal data modeling, but, no studies have done concerning all of the four features simultaneously. In this article, simultaneous Bayesian modeling approach based on a finite mixture of nonlinear mixed-effects Tobit joint (NLMETJ) models with skew distributions is developed to study impact of multiple data features together, and to estimate not only model parameters but also class membership probabilities at both population and individual levels. Simulation studies are conducted to assess the performance of the proposed method, and real data example is analyzed to demonstrate the proposed methodologies through comparing potential models with different specifications of error distributions and various scenarios.


Bayesian inference, left censoring, longitudinal data analysis, measurement errors, mixture of hierarchical Tobit joint models, skew distributions

2010 Mathematics Subject Classification

Primary 62F15. Secondary 62P10.

Published 30 May 2017