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Binary quantile regression: A Bayesian approach based on the asymmetric Laplace density

  • D. F. BENOIT


In this article, we develop a Bayesian method for quantile regression in the case of dichotomous response data. The frequentist approach to this type of regression has proven problematic in both optimizing the objective function and making inference on the regression parameters. By accepting additional distributional assumptions on the error terms, the Bayesian method proposed sets the problem in a parametric framework in which these problems are avoided, i.e. it is relatively straightforward to calculate point predictions of the estimators with their corresponding credible intervals. To test the applicability of the method, we ran two Monte-Carlo experiments and applied it to Horowitz’ (1993) often studied work-trip mode choice dataset. Compared to previous estimates for the latter dataset, the method proposed interestingly leads to a different economic interpretation.

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Paper provided by Ghent University, Faculty of Economics and Business Administration in its series Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium with number 10/662.

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Length: 34 pages
Date of creation: Aug 2010
Date of revision:
Handle: RePEc:rug:rugwps:10/662
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  1. Florios, Kostas & Skouras, Spyros, 2008. "Exact computation of max weighted score estimators," Journal of Econometrics, Elsevier, vol. 146(1), pages 86-91, September.
  2. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
  3. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November.
  4. 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.
  5. Yu, Keming & Stander, Julian, 2007. "Bayesian analysis of a Tobit quantile regression model," Journal of Econometrics, Elsevier, vol. 137(1), pages 260-276, March.
  6. J.A.F. Machado & J. M. C. Santos Silva, 2003. "Quantiles for Counts," Econometrics 0303001, EconWPA.
  7. 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.
  8. 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.
  9. 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.
  10. Yulia Kotlyarova & Victoria Zinde-Walsh, 2006. "Non And Semi-Parametric Estimation In Models With Unknown Smoothness," Departmental Working Papers 2006-15, McGill University, Department of Economics.
  11. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
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