Handling multicollinearity in quantile regression through the use of principal component regression

In many fields of applications, linear regression is the most widely used statistical method to analyze the effect of a set of explanatory variables on a response variable of interest. Classical least squares regression focuses on the conditional mean of the response, while quantile regression extends the view to conditional quantiles. Quantile regression is very convenient, whereas classical parametric assumptions do not hold and/or when relevant information lies in the tails and therefore the interest is in modeling the conditional distribution of the response at locations different from the mean. A situation common to most regression applications is the presence of strong correlations between predictors. This leads to the well-known problem of collinearity. While the effects of collinearity on least squares estimates are well investigated, this is not the case for quantile regression estimates. This paper aims to explore the collinearity problem in quantile regression. First, a simulation study analyses the problem concerning different degrees of collinearity and various response distributions. Then the paper proposes using regression on latent components as a possible solution to collinearity in quantile regression. Finally, a case study shows the assessment of the quality of service in the presence of highly correlated predictors.