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Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data

Author

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  • Xiaoning Li

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

  • Mulati Tuerde

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

  • Xijian Hu

    (College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China)

Abstract

Quantile regression models are remarkable structures for conducting regression analyses when the data are subject to missingness. Missing values occur because of various factors like missing completely at random, missing at random, or missing not at random. All these may result from system malfunction during data collection or human error during data preprocessing. Nevertheless, it is important to deal with missing values before analyzing data since ignoring or omitting missing values may result in biased or misinformed analysis. This paper studies quantile regressions from a Bayesian perspective. By proposing a hierarchical model framework, we develop an alternative approach based on deterministic variational Bayes approximations. Logistic and probit models are adopted to specify propensity scores for missing manifests and covariates, respectively. Bayesian variable selection method is proposed to recognize significant covariates. Several simulation studies and real examples illustrate the advantages of the proposed methodology and offer some possible future research directions.

Suggested Citation

  • Xiaoning Li & Mulati Tuerde & Xijian Hu, 2023. "Variational Bayesian Inference for Quantile Regression Models with Nonignorable Missing Data," Mathematics, MDPI, vol. 11(18), pages 1-31, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3926-:d:1240627
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    References listed on IDEAS

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    1. Baur, Dirk G. & Dimpfl, Thomas & Jung, Robert C., 2012. "Stock return autocorrelations revisited: A quantile regression approach," Journal of Empirical Finance, Elsevier, vol. 19(2), pages 254-265.
    2. Rahim Alhamzawi & Keming Yu, 2012. "Variable selection in quantile regression via Gibbs sampling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(4), pages 799-813, August.
    3. Rahim Alhamzawi, 2016. "Bayesian Analysis of Composite Quantile Regression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 358-373, October.
    4. Niansheng Tang & Sy-Miin Chow & Joseph G. Ibrahim & Hongtu Zhu, 2017. "Bayesian Sensitivity Analysis of a Nonlinear Dynamic Factor Analysis Model with Nonparametric Prior and Possible Nonignorable Missingness," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 875-903, December.
    5. Roger W. Koenker & Vasco D'Orey, 1987. "Computing Regression Quantiles," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 383-393, November.
    6. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
    7. Ying Yuan & Guosheng Yin, 2010. "Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 66(1), pages 105-114, March.
    8. Faes, C. & Ormerod, J. T. & Wand, M. P., 2011. "Variational Bayesian Inference for Parametric and Nonparametric Regression With Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 959-971.
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