Robust Bootstrap Approach to Estimate Bias and RMSE of Indirect Effects in Mediation Analysis

Since its introduction by Efron [1], the bootstrap has been the object of research in statistics. We proposed a new bootstrap procedure of indirect effect in mediation model which is resistant to outliers. The proposed approach was based on residual bootstrap which incorporated rescaled studentized residuals, namely the Rescaled Studentized Residual Bootstrap using Least Squares (ReSRB). The simulation results signify that the ReSRB has outstanding performances compared to the other methods in the presence of outliers. The ReSRB not only has smaller bias, but also smaller root of mean squares error (RMSE). The results also show that for the contaminated data, the better performance of our proposed method with regard to bias and RMSE did not only happen for small or medium percentage of outliers, but also at large percentage of outliers. The advantages of the ReSRB over other methods are even more apparent in data sets with medium or large percentage of outliers. Key-Words: Mediation analysis, outliers, bootstrap, studentized residuals, indirect effect