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Model selection in binary and tobit quantile regression using the Gibbs sampler

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  • Ji, Yonggang
  • Lin, Nan
  • Zhang, Baoxue

Abstract

A stochastic search variable selection approach is proposed for Bayesian model selection in binary and tobit quantile regression. A simple and efficient Gibbs sampling algorithm was developed for posterior inference using a location-scale mixture representation of the asymmetric Laplace distribution. The proposed approach is then illustrated via five simulated examples and two real data sets. Results show that the proposed method performs very well under a variety of scenarios, such as the presence of a moderately large number of covariates, collinearity and heterogeneity.

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  • Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:827-839
    DOI: 10.1016/j.csda.2011.10.003
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    2. Oh, Man-Suk & Park, Eun Sug & So, Beong-Soo, 2016. "Bayesian variable selection in binary quantile regression," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 177-181.
    3. Fengkai Yang, 2018. "A Stochastic EM Algorithm for Quantile and Censored Quantile Regression Models," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 555-582, August.
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    5. Eoghan O'Neill, 2022. "Type I Tobit Bayesian Additive Regression Trees for Censored Outcome Regression," Papers 2211.07506, arXiv.org, revised Feb 2024.
    6. Bernardi, Mauro & Bottone, Marco & Petrella, Lea, 2018. "Bayesian quantile regression using the skew exponential power distribution," Computational Statistics & Data Analysis, Elsevier, vol. 126(C), pages 92-111.
    7. Benoit, Dries F. & Van den Poel, Dirk, 2017. "bayesQR: A Bayesian Approach to Quantile Regression," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i07).
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    9. Mohamed Ouhourane & Yi Yang & Andréa L. Benedet & Karim Oualkacha, 2022. "Group penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 495-529, September.
    10. Fadel Hamid Hadi ALHUSSEINI, 2017. "New Bayesian Lasso in Tobit Quantile Regression," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 65(6), pages 213-229, June.

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