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Bayesian joint relatively quantile regression of latent ordinal multivariate linear models with application to multirater agreement analysis

Author

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  • YuZhu Tian

    (Northwest Normal University
    Gansu Provincial Research Center for Basic Disciplines of Mathematics and Statistics)

  • ChunHo Wu

    (The Hang Seng University of Hong Kong)

  • ManLai Tang

    (University of Hertfordshire)

  • MaoZai Tian

    (Renmin University of China)

Abstract

In this paper, we propose a Bayesian quantile regression (QR) approach to jointly model multivariate ordinal data. Firstly, a multivariate latent variable model is used to link the multivariate ordinal data and latent continuous responses and the multivariate asymmetric Laplace (MAL) distribution is employed to construct the joint QR-based working likelihood for the considered model. Secondly, adaptive- $$L_{1/2}$$ L 1 / 2 penalization priors of regression parameters are incorporated into the working likelihood to implement high-dimensional Bayesian joint QR inference. Markov Chain Monte Carlo (MCMC) algorithm is utilized to derive the fully conditional posterior distributions of all parameters. Thirdly, Bayesian joint relatively QR estimation approach is recommended to result in more efficient estimation results. Finally, Monte Carlo simulation studies and a real instance analysis of multirater agreement data are presented to illustrate the performance of the proposed Bayesian joint relatively QR approach.

Suggested Citation

  • YuZhu Tian & ChunHo Wu & ManLai Tang & MaoZai Tian, 2025. "Bayesian joint relatively quantile regression of latent ordinal multivariate linear models with application to multirater agreement analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 109(1), pages 85-116, March.
    • Handle: RePEc:spr:alstar:v:109:y:2025:i:1:d:10.1007_s10182-024-00509-y
    DOI: 10.1007/s10182-024-00509-y
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    References listed on IDEAS

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    1. Terrance D. Savitsky & Siddhartha R. Dalal, 2014. "Bayesian non-parametric analysis of multirater ordinal data, with application to prioritizing research goals for prevention of suicide," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(4), pages 539-557, August.
    2. Yu-Zhu Tian & Man-Lai Tang & Mao-Zai Tian, 2021. "Bayesian joint inference for multivariate quantile regression model with L $$_{1/2}$$ 1 / 2 penalty," Computational Statistics, Springer, vol. 36(4), pages 2967-2994, December.
    3. Siamak Ghasemzadeh & Mojtaba Ganjali & Taban Baghfalaki, 2018. "Bayesian quantile regression for analyzing ordinal longitudinal responses in the presence of non-ignorable missingness," METRON, Springer;Sapienza Università di Roma, vol. 76(3), pages 321-348, December.
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    5. Naijun Sha & Benard Owusu Dechi, 2019. "A Bayes Inference for Ordinal Response with Latent Variable Approach," Stats, MDPI, vol. 2(2), pages 1-11, June.
    6. Rainer Hirk & Kurt Hornik & Laura Vana, 2019. "Multivariate ordinal regression models: an analysis of corporate credit ratings," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 507-539, September.
    7. Bhattacharya, Indrabati & Ghosal, Subhashis, 2021. "Bayesian multivariate quantile regression using Dependent Dirichlet Process prior," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
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    9. Luca Zanin, 2022. "Estimating the effects of ESG scores on corporate credit ratings using multivariate ordinal logit regression," Empirical Economics, Springer, vol. 62(6), pages 3087-3118, June.
    10. Yu-Zhu Tian & Man-Lai Tang & Mao-Zai Tian, 2021. "Correction to: Bayesian joint inference for multivariate quantile regression model with L1/2 penalty," Computational Statistics, Springer, vol. 36(4), pages 2995-2995, December.
    11. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
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