What Quantile Regression Does and Doesn't Do: A Commentary on Petscher and Logan (2014)

Abstract

Petscher and Logan's (2014) description of quantile regression (QR) might mislead readers to believe it would estimate the relation between an outcome, y, and one or more predictors, x, at different quantiles of the unconditional distribution of y. However, QR models the conditional quantile function of y given x just as linear regression models the conditional mean function. This article's contribution is twofold: First, it discusses potential consequences of methodological misconceptions and formulations of Petscher and Logan's (2014) presentation by contrasting features of QR and linear regression. Second, it reinforces the importance of correct understanding of QR in empirical research by illustrating similarities and differences in various QR estimators and linear regression using simulated data.