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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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