IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i4p827-839.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311003604
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2011.10.003?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. Komunjer, Ivana, 2005. "Quasi-maximum likelihood estimation for conditional quantiles," Journal of Econometrics, Elsevier, vol. 128(1), pages 137-164, September.
    2. D. F. Benoit & D. Van Den Poel, 2010. "Binary quantile regression: A Bayesian approach based on the asymmetric Laplace density," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/662, Ghent University, Faculty of Economics and Business Administration.
    3. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    4. Moshe Buchinsky & Jinyong Hahn, 1998. "An Alternative Estimator for the Censored Quantile Regression Model," Econometrica, Econometric Society, vol. 66(3), pages 653-672, May.
    5. Das, Sanghamitra, 1991. "A semiparametric structural analysis of the idling of cement kilns," Journal of Econometrics, Elsevier, vol. 50(3), pages 235-256, December.
    6. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    7. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    8. Bartik, Timothy J. & Butler, J. S. & Liu, Jin-Tan, 1992. "Maximum score estimates of the determinants of residential mobility: Implications for the value of residential attachment and neighborhood amenities," Journal of Urban Economics, Elsevier, vol. 32(2), pages 233-256, September.
    9. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    10. Bilias, Yannis & Chen, Songnian & Ying, Zhiliang, 2000. "Simple resampling methods for censored regression quantiles," Journal of Econometrics, Elsevier, vol. 99(2), pages 373-386, December.
    11. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407.
    12. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
    13. Fitzenberger, Bernd & Winker, Peter, 2007. "Improving the computation of censored quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 88-108, September.
    14. Goodwin, Barry K, 1996. "Semiparametric (Distribution-Free) Testing of the Expectations Hypothesis in a Parimutuel Gambling Market," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 487-496, October.
    15. Ana Fernandez & Juan Rodriquez-Poo, 1997. "Estimation and specification testing in female labor participation models: parametric and semiparametric methods," Econometric Reviews, Taylor & Francis Journals, vol. 16(2), pages 229-247.
    16. Calcagno, Vincent & de Mazancourt, Claire, 2010. "glmulti: An R Package for Easy Automated Model Selection with (Generalized) Linear Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i12).
    17. Kottas A. & Gelfand A.E., 2001. "Bayesian Semiparametric Median Regression Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1458-1468, December.
    18. Horowitz, Joel L., 1993. "Semiparametric estimation of a work-trip mode choice model," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 49-70, July.
    19. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    20. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    21. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    22. Wang, Hansheng & Li, Guodong & Jiang, Guohua, 2007. "Robust Regression Shrinkage and Consistent Variable Selection Through the LAD-Lasso," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 347-355, July.
    23. Hanson T. & Johnson W.O., 2002. "Modeling Regression Error With a Mixture of Polya Trees," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1020-1033, December.
    24. Drovandi, Christopher C. & Pettitt, Anthony N., 2011. "Likelihood-free Bayesian estimation of multivariate quantile distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2541-2556, September.
    25. Stephen Walker & Bani K. Mallick, 1999. "A Bayesian Semiparametric Accelerated Failure Time Model," Biometrics, The International Biometric Society, vol. 55(2), pages 477-483, June.
    26. Hideo Kozumi & Genya Kobayashi, 2009. "Gibbs Sampling Methods for Bayesian Quantile Regression," Discussion Papers 2009-02, Kobe University, Graduate School of Business Administration.
    27. Taddy, Matthew A. & Kottas, Athanasios, 2010. "A Bayesian Nonparametric Approach to Inference for Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 357-369.
    28. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    29. Hahn, Jinyong, 1995. "Bootstrapping Quantile Regression Estimators," Econometric Theory, Cambridge University Press, vol. 11(1), pages 105-121, February.
    30. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
    31. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
    32. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    33. Zou, Hui & Yuan, Ming, 2008. "Regularized simultaneous model selection in multiple quantiles regression," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5296-5304, August.
    34. Chib, Siddhartha, 1992. "Bayes inference in the Tobit censored regression model," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 79-99.
    35. Hong H. & Chernozhukov V., 2002. "Three-Step Censored Quantile Regression and Extramarital Affairs," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 872-882, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Danúbia R. Cunha & Jose Angelo Divino & Helton Saulo, 2022. "On a log-symmetric quantile tobit model applied to female labor supply data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(16), pages 4225-4253, December.
    2. 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.
    3. Mohammad Arshad Rahman & Angela Vossmeyer, 2019. "Estimation and Applications of Quantile Regression for Binary Longitudinal Data," Advances in Econometrics, in: Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B, volume 40, pages 157-191, Emerald Group Publishing Limited.
    4. 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.
    5. 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).
    6. Alhamzawi, Rahim, 2016. "Bayesian model selection in ordinal quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 68-78.
    7. 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.
    8. 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.
    9. Eoghan O'Neill, 2022. "Type I Tobit Bayesian Additive Regression Trees for Censored Outcome Regression," Papers 2211.07506, arXiv.org, revised Feb 2024.
    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.

    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. Alhamzawi, Rahim, 2016. "Bayesian model selection in ordinal quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 68-78.
    2. Genya Kobayashi & Hideo Kozumi, 2012. "Bayesian analysis of quantile regression for censored dynamic panel data," Computational Statistics, Springer, vol. 27(2), pages 359-380, June.
    3. Xianhua Dai & Wolfgang Karl Härdle & Keming Yu, 2016. "Do maternal health problems influence child's worrying status? Evidence from the British Cohort Study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2941-2955, December.
    4. Alhamzawi, Rahim & Yu, Keming, 2013. "Conjugate priors and variable selection for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 209-219.
    5. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    6. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407, April.
    7. repec:hum:wpaper:sfb649dp2014-021 is not listed on IDEAS
    8. Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    9. Hideo Kozumi & Genya Kobayashi, 2009. "Gibbs Sampling Methods for Bayesian Quantile Regression," Discussion Papers 2009-02, Kobe University, Graduate School of Business Administration.
    10. D. F. Benoit & D. Van Den Poel, 2010. "Binary quantile regression: A Bayesian approach based on the asymmetric Laplace density," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/662, Ghent University, Faculty of Economics and Business Administration.
    11. R. Alhamzawi & K. Yu & D. F. Benoit, 2011. "Bayesian adaptive Lasso quantile regression," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 11/728, Ghent University, Faculty of Economics and Business Administration.
    12. 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.
    13. Yunwen Yang & Huixia Judy Wang & Xuming He, 2016. "Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood," International Statistical Review, International Statistical Institute, vol. 84(3), pages 327-344, December.
    14. Bilias, Yannis & Florios, Kostas & Skouras, Spyros, 2019. "Exact computation of Censored Least Absolute Deviations estimator," Journal of Econometrics, Elsevier, vol. 212(2), pages 584-606.
    15. Bernd Fitzenberger & Ralf Wilke, 2006. "Using quantile regression for duration analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 105-120, March.
    16. Joel L. Horowitz, 2018. "Bootstrap methods in econometrics," CeMMAP working papers CWP53/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Rima Rajab & Milan Dražić & Nenad Mladenović & Pavle Mladenović & Keming Yu, 2015. "Fitting censored quantile regression by variable neighborhood search," Journal of Global Optimization, Springer, vol. 63(3), pages 481-500, November.
    18. 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.
    19. Kim, Mo Se & Lee, Byung Sung & Lee, Hye Seon & Lee, Seung Ho & Lee, Junseok & Kim, Wonse, 2020. "Robust estimation of outage costs in South Korea using a machine learning technique: Bayesian Tobit quantile regression," Applied Energy, Elsevier, vol. 278(C).
    20. Joel L. Horowitz, 2018. "Bootstrap Methods in Econometrics," Papers 1809.04016, arXiv.org.
    21. Rahim Alhamzawi, 2016. "Bayesian Analysis of Composite Quantile Regression," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 8(2), pages 358-373, October.

    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:eee:csdana:v:56:y:2012:i:4:p:827-839. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.