Valid Standard Errors for Bayesian Quantile Regression With Clustered and Independent Data

Abstract

Bayesian quantile regression typically uses the asymmetric Laplace distribution as working likelihood, not because it is a plausible data-generating distribution but because the corresponding maximum likelihood estimator is identical to the classical estimator by Koenker and Bassett. While point estimation is consistent, credible intervals tend to have poor frequentist coverage. We propose using infinitesimal jackknife (IJ) standard errors introduced by Giordano and Broderick, which do not require resampling and can be obtained from a single Markov chain Monte Carlo run. Simulations and applications to real data show that IJ standard errors have good frequentist properties for both independent and clustered data. We provide an R package, IJSE, that computes IJ standard errors after estimation of any model with the brms wrapper for Stan.