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Robust Bayesian cumulative probit linear mixed models for longitudinal ordinal data

Author

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  • Kuo-Jung Lee

    (National Cheng Kung University)

  • Ray-Bing Chen

    (National Cheng Kung University)

  • Keunbaik Lee

    (Sungkyunkwan University)

Abstract

Longitudinal studies have been conducted in various fields, including medicine, economics and the social sciences. In this paper, we focus on longitudinal ordinal data. Since the longitudinal data are collected over time, repeated outcomes within each subject may be serially correlated. To address both the within-subjects serial correlation and the specific variance between subjects, we propose a Bayesian cumulative probit random effects model for the analysis of longitudinal ordinal data. The hypersphere decomposition approach is employed to overcome the positive definiteness constraint and high-dimensionality of the correlation matrix. Additionally, we present a hybrid Gibbs/Metropolis-Hastings algorithm to efficiently generate cutoff points from truncated normal distributions, thereby expediting the convergence of the Markov Chain Monte Carlo (MCMC) algorithm. The performance and robustness of our proposed methodology under misspecified correlation matrices are demonstrated through simulation studies under complete data, missing completely at random (MCAR), and missing at random (MAR). We apply the proposed approach to analyze two sets of actual ordinal data: the arthritis dataset and the lung cancer dataset. To facilitate the implementation of our method, we have developed BayesRGMM, an open-source R package available on CRAN, accompanied by comprehensive documentation and source code accessible at https://github.com/kuojunglee/BayesRGMM/ .

Suggested Citation

  • Kuo-Jung Lee & Ray-Bing Chen & Keunbaik Lee, 2025. "Robust Bayesian cumulative probit linear mixed models for longitudinal ordinal data," Computational Statistics, Springer, vol. 40(1), pages 441-468, January.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01499-w
    DOI: 10.1007/s00180-024-01499-w
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    References listed on IDEAS

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    1. Guanyu Hu & Ming-Hui Chen & Nalini Ravishanker, 2023. "Bayesian analysis of spherically parameterized dynamic multivariate stochastic volatility models," Computational Statistics, Springer, vol. 38(2), pages 845-869, June.
    2. Keunbaik Lee & Hyunsoon Cho & Min‐Sun Kwak & Eun Jin Jang, 2020. "Estimation of covariance matrix of multivariate longitudinal data using modified Choleksky and hypersphere decompositions," Biometrics, The International Biometric Society, vol. 76(1), pages 75-86, March.
    3. Weiping Zhang & Chenlei Leng & Cheng Yong Tang, 2015. "A joint modelling approach for longitudinal studies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 219-238, January.
    4. Ruey S. Tsay & Mohsen Pourahmadi, 2017. "Modelling structured correlation matrices," Biometrika, Biometrika Trust, vol. 104(1), pages 237-242.
    5. Keunbaik Lee & Michael J. Daniels, 2007. "A Class of Markov Models for Longitudinal Ordinal Data," Biometrics, The International Biometric Society, vol. 63(4), pages 1060-1067, December.
    Full references (including those not matched with items on IDEAS)

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