Research Article
Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution
SUMMARY
This paper develops a Bayesian method for quantile regression for dichotomous response data. The frequentist approach to this type of regression has proven problematic in both optimizing the objective function and making inferences on the 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. To test the applicability of the method, we ran two Monte Carlo experiments and applied it to Horowitz's (1993) often studied work‐trip mode choice dataset. Compared to previous estimates for the latter dataset, the method proposed leads to a different economic interpretation. Copyright © 2010 John Wiley & Sons, Ltd.
Citing Literature
Number of times cited according to CrossRef: 42
- J.-L. Dortet-Bernadet, Y. Fan, T. Rodrigues, Bayesian quantile regression with the asymmetric Laplace distribution, Flexible Bayesian Regression Modelling, 10.1016/B978-0-12-815862-3.00007-X, (1-25), (2020).
- Georges Bresson, Guy Lacroix, Mohammad Arshad Rahman, Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada, Empirical Economics, 10.1007/s00181-020-01893-5, (2020).
- Le-Yu Chen, Sokbae Lee, Binary classification with covariate selection through ℓ0-penalised empirical risk minimisation, The Econometrics Journal, 10.1093/ectj/utaa017, (2020).
- A Ford Ramsey, Probability Distributions of Crop Yields: A Bayesian Spatial Quantile Regression Approach, American Journal of Agricultural Economics, 10.1093/ajae/aaz029, 102, 1, (220-239), (2019).
- Josephine Merhi Bleik, Fully Bayesian Estimation of Simultaneous Regression Quantiles under Asymmetric Laplace Distribution Specification, Journal of Probability and Statistics, 10.1155/2019/8610723, 2019, (1-12), (2019).
- Haider Kadhim Abbas Hilali, Rahim Alhamzawi, Bayesian Adaptive Lasso binary regression with ridge parameter, Journal of Physics: Conference Series, 10.1088/1742-6596/1294/3/032036, 1294, (032036), (2019).
- Yves Stephan Schüler, The Impact of Uncertainty and Certainty Shocks, SSRN Electronic Journal, 10.2139/ssrn.3409697, (2019).
- Matthias Schlögl, Rainer Stütz, Gregor Laaha, Michael Melcher, A comparison of statistical learning methods for deriving determining factors of accident occurrence from an imbalanced high resolution dataset, Accident Analysis & Prevention, 10.1016/j.aap.2019.02.008, 127, (134-149), (2019).
- Mohammad Arshad Rahman, Angela Vossmeyer, Estimation and Applications of Quantile Regression for Binary Longitudinal Data, Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B, 10.1108/S0731-90532019000040B009, (157-191), (2019).
- Xuecai Xu, Xiangjian Luo, Daiquan Xiao, S. C. Wong, Comparative analysis of Bayesian quantile regression models for pedestrian injury severity at signalized intersections, Journal of Transportation Safety & Security, 10.1080/19439962.2019.1703867, (1-22), (2019).
- Xiao Lu, Discrete Choice Data with Unobserved Heterogeneity: A Conditional Binary Quantile Model, Political Analysis, 10.1017/pan.2019.29, (1-21), (2019).
- Katerina Aristodemou, Jian He, Keming Yu, Binary quantile regression and variable selection: A new approach, Econometric Reviews, 10.1080/07474938.2017.1417701, 38, 6, (679-694), (2018).
- Kostas Florios, A hyperplanes intersection simulated annealing algorithm for maximum score estimation, Econometrics and Statistics, 10.1016/j.ecosta.2017.03.005, 8, (37-55), (2018).
- Zakariya Yahya Algamal, Rahim Alhamzawi, Haithem Taha Mohammad Ali, Gene selection for microarray gene expression classification using Bayesian Lasso quantile regression, Computers in Biology and Medicine, 10.1016/j.compbiomed.2018.04.018, 97, (145-152), (2018).
- Emmanuel Tsyawo, Recovering Distributions for the Estimation of Treatment Effects Under Partly Unobserved Treatment with Repeated Cross-Sections, SSRN Electronic Journal, 10.2139/ssrn.3194286, (2018).
- Le-Yu Chen, Sokbae Lee, Best subset binary prediction, Journal of Econometrics, 10.1016/j.jeconom.2018.05.001, 206, 1, (39-56), (2018).
- Mauro Bernardi, Marco Bottone, Lea Petrella, Bayesian quantile regression using the skew exponential power distribution, Computational Statistics & Data Analysis, 10.1016/j.csda.2018.04.008, 126, (92-111), (2018).
- Peter Congdon, Quantile regression for overdispersed count data: a hierarchical method, Journal of Statistical Distributions and Applications, 10.1186/s40488-017-0073-4, 4, 1, (2017).
- undefined, Proceedings of the 10th Annual ACM India Compute Conference on ZZZ - Compute '17, 10.1145/3140107.3140122, (109-113), (2017).
- V L Miguéis, D F Benoit, D Van den Poel, Enhanced decision support in credit scoring using Bayesian binary quantile regression, Journal of the Operational Research Society, 10.1057/jors.2012.116, 64, 9, (1374-1383), (2017).
- Felipe Vásquez Lavín, Ricardo Flores, Verónica Ibarnegaray, A Bayesian quantile binary regression approach to estimate payments for environmental services, Environment and Development Economics, 10.1017/S1355770X16000255, 22, 2, (156-176), (2016).
- Yukiko Omata, Hajime Katayama, Toshi. H. Arimura, Same concerns, same responses? A Bayesian quantile regression analysis of the determinants for supporting nuclear power generation in Japan, Environmental Economics and Policy Studies, 10.1007/s10018-016-0167-0, 19, 3, (581-608), (2016).
- Cristina Mollica, Lea Petrella, Bayesian binary quantile regression for the analysis of Bachelor-to-Master transition, Journal of Applied Statistics, 10.1080/02664763.2016.1263835, 44, 15, (2791-2812), (2016).
- Man-Suk Oh, Eun Sug Park, Beong-Soo So, Bayesian variable selection in binary quantile regression, Statistics & Probability Letters, 10.1016/j.spl.2016.07.001, 118, (177-181), (2016).
- Dries F. Benoit, Stefan Van Aelst, Dirk Van den Poel, Outlier‐Robust Bayesian Multinomial Choice Modeling, Journal of Applied Econometrics, 10.1002/jae.2482, 31, 7, (1445-1466), (2015).
- Yunwen Yang, Huixia Judy Wang, Xuming He, Posterior Inference in Bayesian Quantile Regression with Asymmetric Laplace Likelihood, International Statistical Review, 10.1111/insr.12114, 84, 3, (327-344), (2015).
- Yifan Wang, Xiang-Nan Feng, Xin-Yuan Song, Bayesian Quantile Structural Equation Models, Structural Equation Modeling: A Multidisciplinary Journal, 10.1080/10705511.2015.1033057, 23, 2, (246-258), (2015).
- B. Dima, Ş. M. Dima, Income Distribution and Social Tolerance, Social Indicators Research, 10.1007/s11205-015-1038-y, 128, 1, (439-466), (2015).
- Karthik Sriram, R. V. Ramamoorthi, Pulak Ghosh, On Bayesian Quantile Regression Using a Pseudo-joint Asymmetric Laplace Likelihood, Sankhya A, 10.1007/s13171-015-0079-2, 78, 1, (87-104), (2015).
- Hussein Hashem, Veronica Vinciotti, Rahim Alhamzawi, Keming Yu, Quantile regression with group lasso for classification, Advances in Data Analysis and Classification, 10.1007/s11634-015-0206-x, 10, 3, (375-390), (2015).
- Karthik Sriram, A sandwich likelihood correction for Bayesian quantile regression based on the misspecified asymmetric Laplace density, Statistics & Probability Letters, 10.1016/j.spl.2015.07.035, 107, (18-26), (2015).
- Yukiko Omata, Hajime Katayama, Toshi H. Arimura, Same Concerns, Same Responses? A Bayesian Quantile Regression Analysis of the Determinants for Supporting Nuclear Power Generation in Japan, SSRN Electronic Journal, 10.2139/ssrn.2692881, (2015).
- Chiuling Lu, Ann Shawing Yang, Jui-Feng Huang, Bankruptcy predictions for U.S. air carrier operations: a study of financial data, Journal of Economics and Finance, 10.1007/s12197-014-9282-6, 39, 3, (574-589), (2014).
- Rahim Alhamzawi, Keming Yu, Bayesian Tobit quantile regression using g -prior distribution with ridge parameter , Journal of Statistical Computation and Simulation, 10.1080/00949655.2014.945449, 85, 14, (2903-2918), (2014).
- Bruno Santos, Heleno Bolfarine, Bayesian analysis for zero-or-one inflated proportion data using quantile regression, Journal of Statistical Computation and Simulation, 10.1080/00949655.2014.986733, 85, 17, (3579-3593), (2014).
- Mingxiang Li, Moving Beyond the Linear Regression Model, Journal of Management, 10.1177/0149206314551963, 41, 1, (71-98), (2014).
- Rahim Alhamzawi, Model selection in quantile regression models, Journal of Applied Statistics, 10.1080/02664763.2014.959905, 42, 2, (445-458), (2014).
- Dries F. Benoit, Rahim Alhamzawi, Keming Yu, Bayesian lasso binary quantile regression, Computational Statistics, 10.1007/s00180-013-0439-0, 28, 6, (2861-2873), (2013).
- Yonggang Ji, Nan Lin, Baoxue Zhang, Model selection in binary and tobit quantile regression using the Gibbs sampler, Computational Statistics & Data Analysis, 10.1016/j.csda.2011.10.003, 56, 4, (827-839), (2012).
- Ali Alkenani, Rahim Alhamzawi, Keming Yu, Penalized Flexible Bayesian Quantile Regression, Applied Mathematics, 10.4236/am.2012.312A296, 03, 12, (2155-2168), (2012).
- Rahim Alhamzawi, Keming Yu, Dries F Benoit, Bayesian adaptive Lasso quantile regression, Statistical Modelling: An International Journal, 10.1177/1471082X1101200304, 12, 3, (279-297), (2012).
- Kostas Florios, Application of the Maximum Score/Maximum Profit Bi-Objective Estimator to Stocks of the Banking Sector in the Athens Stock Exchange, SSRN Electronic Journal, 10.2139/ssrn.1740717, (2011).
