Bayesian relative composite quantile regression with ordinal longitudinal data and some case studies

ABSTRACT

In real applied fields such as clinical medicine, environmental sciences, psychology as well as economics, we often encounter the task of conducting statistical inference for longitudinal data with ordinal responses. The traditional methods of longitudinal data analysis are often inclined to model continuous responses, which are no longer suitable for such ordinal data. Logistic regression and probit regression are two considerable methods which are frequently used to model ordinal longitudinal responses. However, such modelling methods just depict the mean feature of latent outcome variable and may produce non-robust results when encountering nor-normal errors or outliers. As a proper alternative of mean regression models, composite quantile regression (CQR) method is usually employed to derive robust estimation. The target of this paper is to investigate the CQR estimation approach for ordinal latent longitudinal model. The joint Bayesian hierarchical model is established and a relative CQR estimation approach is suggested to conduct posterior inference for the considered model. Further, in longitudinal data modelling, excessive predictors may be brought into in the models which result in the decrease of the model prediction precision. Bayesian $L_{1/2}$ regularized prior is incorporated into ordinal longitudinal CQR model to conduct variable selection simultaneously. Finally, simulation studies and two ordinal longitudinal data analysis are hired to illustrate the considered method.

KEYWORDS:

• Ordinal longitudinal
• Relative CQR
• MCMC sampling
• Cut-points
• $L_{1/2}$ regularization
• Psychiatric data

Acknowledgments

Authors thank editors and referees for their constructive comments and suggestions which have greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Yu-Zhu Tian was supported by grants from the National Natural Science Foundation of China (grant 12061065) and Funds for Innovative Fundamental Research Group Project of Gansu Province of China (grant 23JRRA684). The work of Man-Lai Tang is partially supported by the Research Matching Grant (700006) and FDS Grant (UGC/FDS14/P05/20) from the Research Grants Council of the Hong Kong Special Administration Region and the Big Data Intelligence Center in The Hang Seng University of Hong Kong.