Quantile ridge beta regression model and Bayesian regularized quantile beta regression for solving the skewness and improving the accuracy of the model selection in bounded data

Abstract

Skewed distributions have an additional shape parameter that represents the direction of the asymmetry in the density. If skewness in observations is ignored, statistical inferences based on symmetric distributions may yield biased or even misleading conclusions. Bayesian regularized quantile regression (BRQR) is effective in quantile regression for addressing skewness. Additionally, quantile ridge regression (QRR) has been developed for variable selection and to address multicollinearity among predictor variables. Most studies have used the asymmetric Laplace distribution (ALD) to address skewness, but this solution is not useful for bounded data because it has unbounded support, allowing values far in either direction and potentially violating the bounded-data assumption. The hybrid Bayesian regularized quantile beta regression--quantile ridge beta regression (BRQBR--QRBR) model is proposed for analyzing bounded data within the interval (0,1) with skewness while improving model-selection accuracy. The proposed model applies BRQBR to the skewed, bounded data to address skewness and then uses QRBR to improve model accuracy. Simulation studies and real-dataset applications were conducted. The results show that the proposed BRQBR--QRBR method, in most cases, outperforms the original method by improving prediction accuracy through skewness correction.