MODEL SELECTION VIA ROBUST VERSION OF R-SQUARED

Abstract

R-squared (R²) is a popular method for variable selection in linear regression models. R² based on Least Squares (LS) regression minimizes the sum of the squared residuals; LS is sensitive to outlier observation. Alternative criterion based on M-estimators, which is less sensitive to outlying observation has been proposed. In this study explicit expression for such criterion is obtained when the Least Trimmed Squares (LTS) estimator is used. The influence function of R² is also discussed. In our simulation study, the performance of proposed criterion is compared to the existing criteria based on M-estimators (R²_M) and to the classical non-robust based on least squares estimators (R2_LS). We observe that the proposed (R²_LTS) selects more appropriate models in the case of bad leverage points (outliers in the X-direction) are present.