IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v40y2025i1d10.1007_s00180-024-01499-w.html
   My bibliography  Save this article

Robust Bayesian cumulative probit linear mixed models for longitudinal ordinal data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-024-01499-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-024-01499-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rhee, Anbin & Kwak, Min-Sun & Lee, Keunbaik, 2022. "Robust modeling of multivariate longitudinal data using modified Cholesky and hypersphere decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 170(C).
    2. Lee, Keunbaik & Choi, Jongwoo & Jang, Eun Jin & Dey, Dipak, 2025. "Multivariate robust linear models for multivariate longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 206(C).
    3. Lee, Keunbaik & Lee, Chang-Hoon & Kwak, Min-Sun & Jang, Eun Jin, 2021. "Analysis of multivariate longitudinal data using ARMA Cholesky and hypersphere decompositions," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    4. Rana, Subrata & Roy, Surupa & Das, Kalyan, 2018. "Analysis of ordinal longitudinal data under nonignorable missingness and misreporting: An application to Alzheimer’s disease study," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 62-77.
    5. Lee, Keunbaik & Sohn, Insuk & Kim, Donguk, 2016. "Analysis of long series of longitudinal ordinal data using marginalized models," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 363-371.
    6. Jia Chen & Degui Li & Yingcun Xia, 2015. "New Semiparametric Estimation Procedure for Functional Coefficient Longitudinal Data Models," Discussion Papers 15/17, Department of Economics, University of York.
    7. Zhang, Lin & Chen, Xiaohui & Khatab, Abdelhakim & An, Youjun & Feng, XiaoNing, 2024. "Joint optimization of selective maintenance and repairpersons assignment problem for mission-oriented systems operating under s-dependent competing risks," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    8. Ruey S. Tsay & Mohsen Pourahmadi, 2017. "Modelling structured correlation matrices," Biometrika, Biometrika Trust, vol. 104(1), pages 237-242.
    9. Wei Liu & Bo Zhang & Zhiwei Zhang & Xiao-Hua Zhou, 2013. "Joint Modeling of Transitional Patterns of Alzheimer's Disease," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-11, September.
    10. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    11. Lee, Keunbaik & Joo, Yongsung, 2019. "Marginalized models for longitudinal count data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 47-58.
    12. Weiping Zhang & Feiyue Xie & Jiaxin Tan, 2020. "A robust joint modeling approach for longitudinal data with informative dropouts," Computational Statistics, Springer, vol. 35(4), pages 1759-1783, December.
    13. Chen, Jia & Li, Degui & Xia, Yingcun, 2019. "Estimation of a rank-reduced functional-coefficient panel data model with serial correlation," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 456-479.
    14. Singh, Ashutosh & Bag, Surajit & Choi, Tsan-Ming & Munjal, Surender, 2024. "Managing risk concerns with ordered backlogs in the semiconductor industry: An empirical study," International Journal of Production Economics, Elsevier, vol. 275(C).
    15. Yixin Chen & Weixin Yao, 2017. "Unified Inference for Sparse and Dense Longitudinal Data in Time-varying Coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 268-284, March.
    16. 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.
    17. Qingze Li & Jianxin Pan, 2022. "Permutation Variation and Alternative Hyper-Sphere Decomposition," Mathematics, MDPI, vol. 10(4), pages 1-19, February.
    18. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    19. Wagner Hugo Bonat & Bent Jørgensen, 2016. "Multivariate covariance generalized linear models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(5), pages 649-675, November.
    20. Lee, Keunbaik & Baek, Changryong & Daniels, Michael J., 2017. "ARMA Cholesky factor models for the covariance matrix of linear models," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 267-280.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01499-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.