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Bayesian lasso binary quantile regression

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  • Dries Benoit
  • Rahim Alhamzawi

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  • Keming Yu
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    Abstract

    In this paper, a Bayesian hierarchical model for variable selection and estimation in the context of binary quantile regression is proposed. Existing approaches to variable selection in a binary classification context are sensitive to outliers, heteroskedasticity or other anomalies of the latent response. The method proposed in this study overcomes these problems in an attractive and straightforward way. A Laplace likelihood and Laplace priors for the regression parameters are proposed and estimated with Bayesian Markov Chain Monte Carlo. The resulting model is equivalent to the frequentist lasso procedure. A conceptional result is that by doing so, the binary regression model is moved from a Gaussian to a full Laplacian framework without sacrificing much computational efficiency. In addition, an efficient Gibbs sampler to estimate the model parameters is proposed that is superior to the Metropolis algorithm that is used in previous studies on Bayesian binary quantile regression. Both the simulation studies and the real data analysis indicate that the proposed method performs well in comparison to the other methods. Moreover, as the base model is binary quantile regression, a much more detailed insight in the effects of the covariates is provided by the approach. An implementation of the lasso procedure for binary quantile regression models is available in the R-package bayesQR. Copyright Springer-Verlag Berlin Heidelberg 2013

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    File URL: http://hdl.handle.net/10.1007/s00180-013-0439-0
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    Bibliographic Info

    Article provided by Springer in its journal Computational Statistics.

    Volume (Year): 28 (2013)
    Issue (Month): 6 (December)
    Pages: 2861-2873

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    Handle: RePEc:spr:compst:v:28:y:2013:i:6:p:2861-2873

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    Related research

    Keywords: Binary; Quantile regression; Gibbs sampler; Lasso; Variable selection;

    References

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, October.
    3. 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.
    4. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    5. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    6. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    7. Dries F. Benoit & Dirk Van den Poel, 2012. "Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(7), pages 1174-1188, November.
    8. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
    9. Tony Lancaster & Sung Jae Jun, 2010. "Bayesian quantile regression methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(2), pages 287-307.
    10. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407.
    11. 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.
    12. 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.
    13. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    14. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
    15. 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.
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