Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach

Abstract

In this paper, a joint model for analyzing multivariate mixed ordinal and continuous responses, where continuous outcomes may be skew, is presented. For modeling the discrete ordinal responses, a continuous latent variable approach is considered and for describing continuous responses, a skew-normal mixed effects model is used. A Bayesian approach using Markov Chain Monte Carlo (MCMC) is adopted for parameter estimation. Some simulation studies are performed for illustration of the proposed approach. The results of the simulation studies show that the use of the separate models or the normal distributional assumption for shared random effects and within-subject errors of continuous and ordinal variables, instead of the joint modeling under a skew-normal distribution, leads to biased parameter estimates. The approach is used for analyzing a part of the British Household Panel Survey (BHPS) data set. Annual income and life satisfaction are considered as the continuous and the ordinal longitudinal responses, respectively. The annual income variable is severely skewed, therefore, the use of the normality assumption for the continuous response does not yield acceptable results. The results of data analysis show that gender, marital status, educational levels and the amount of money spent on leisure have a significant effect on annual income, while marital status has the highest impact on life satisfaction.

Keywords:

• Bayesian approach
• joint modeling
• multivariate longitudinal data
• Markov Chain MonteCarlo
• mixed ordinal and continues responses
• skew-normal distribution

Acknowledgments

The author thanks the referee for a number of helpful suggestions for improvement of the article.

Disclosure statement

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

Funding

This research project has been financially supported by the Office of Vice Chancellor of Islamic Azad University, Roudehen Branch [91/14438].

Notes

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