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

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.