Implementation of Yeo-Johnson Transformation in Quantile Regression

Abstract

Power transformations offer a remedy for retaining the symmetry, homoscedasticity and normality assumptions that is typical of regression analysis. The Box-Cox power transformation is defined for a strictly positive response variable in regression model. In this work the Yeo-Johnson quantile regression model is investigated as a modification of Box-Cox quantile regression model to accommodate both negative and positive values of the response variable, while implementing the two-step method of estimation of the transformation parameter. The quantile regression without any transformation was also considered. The study examines the adequacy of the Yeo-Johnson quantile regression over the quantile regression. The results demonstrate that the Yeo-Johnson quantile regression model performed better that the quantile regression model at all quantiles considered in this paper. Comparison of both models was done using the Akaike Information criteria (AIC) and the mean square error (MSE) as the comparison criteria.