Quantile regression

What is quantile regression

Quantile regression keeps growing in importance and interest since it was introduced by Koenker and Basset in 1978. The method popularity among the practitioners and also researchers’ community is without doubt due to its peculiarity to provide them a realistic framework to perform their studies.

Indeed, by nature, quantile regression enables to work with a wide range of distributions, without being subject to any restrictions such as normality assumption, thus contrasting with usual regression.

As a consequence of that flexibility, many fields find great interest in quantile regression including Economics, Social Sciences, Environments, Biometrics and Behavioral Sciences, among others.

The specificity of Quantile Regression with respect to other methods is to provide an estimate of conditional quantiles of the dependent variable instead of conditional mean. In this way, Quantile Regression permits to give a more accurate qualityassessment based on a quantile analysis.  

The parameter estimates in QR linear models have the same interpretation as those of any other linear model, as rates of change. Therefore, in a similar way to the ordinary least squares (OLS) model, the coefficients of the QR model can be interpreted as the rate of change of some quantile of the dependent variable distribution per unit change in the value of some regressor.

Moreover, as in ANCOVA, it’s possible to mix qualitative and quantitative explanatory variables. In three other tutorials on linear regression this dataset is also used, with the Height (Linear Regression), the Height and the Age (ANOVA) and then the Height, the Age and the Gender (ANCOVA) as explanatory variables.