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Bayesian analysis of multivariate mixed models for a prospective cohort study using skew-elliptical distributions

Authors

  • Iraj Kazemi,

    Corresponding author
    • Department of Statistics, College of Science, University of Isfahan, Isfahan, Iran
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  • Zahra Mahdiyeh,

    1. Department of Statistics, College of Science, University of Isfahan, Isfahan, Iran
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  • Marjan Mansourian,

    1. Department of Biostatistics and Epidemiology, Health School, Isfahan University of Medical Sciences, Isfahan, Iran
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  • Jongbae J. Park

    1. Asian Medicine & Acupuncture Research, Department of Physical Medicine and Rehabilitation, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC, USA
    2. Regional Center for Neurosensory Disorders, Orofacial Pain Program, UNC School of Dentistry, Chapel Hill, NC, USA
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Corresponding author: e-mail: i.kazemi@stat.ui.ac.ir, Phone: +98-311-7934600, Fax: +98-311-7934601

Abstract

Classical multivariate mixed models that acknowledge the correlation of patients through the incorporation of normal error terms are widely used in cohort studies. Violation of the normality assumption can make the statistical inference vague. In this paper, we propose a Bayesian parametric approach by relaxing this assumption and substituting some flexible distributions in fitting multivariate mixed models. This strategy allows for the skewness and the heavy tails of error-term distributions and thus makes inferences robust to the violation. This approach uses flexible skew-elliptical distributions, including skewed, fat, or thin-tailed distributions, and imposes the normal model as a special case. We use real data obtained from a prospective cohort study on the low back pain to illustrate the usefulness of our proposed approach.

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