Binary quantile regression: a Bayesian approach based on the asymmetric Laplace distribution

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.