A simulation study of weighted structural regression methods in the presence of outlier

Weighted Structural Regression (WSR) (Pruzek & Lepak, 1992) constitutes a broad class of regression methods that has been shown to provide several advantages over Ordinary Least Squares (OLS) regression in situations where a relatively parsimonious common factor model can approximately reproduce the original correlation matrix. Five specific regression methods within the WSR class were compared to one another, viz.: Ordinary Least Squares, Minimum Risk Ridge, Minimum Risk, Minimum Risk*2, GFI, and Reduced Rank Regression. Simulation methods were used to compare these methods on the basis of regression weight stability, expected predicted mean squared errors, and score estimation accuracy in the presence of outlier contamination.;Five population structures (four real & one synthetic) were used, as well as two levels of outlier contamination (2% & 5%), three different common factor structures, and two sample sizes (60 & 120). The non-OLS WSR methods were compared to OLS regression in terms of their ability to reproduce known population regression weights and score values in the presence of data contamination. The data contamination method was such as to produce relatively mild outliers, ones that tend to be difficult to detect by conventional means; this resulted in heavier than normal tails in a predetermined percentage of rows of the simulated data for each population system. Results for each of the three MSE criteria were based on one hundred bootstrap samples for each experimental condition.;The results showed that three of the WSR methods, those that used adaptive weighting functions, performed especially well. The Minimum Risk*2 method in particular worked much better than Ordinary Least Squares regression with respect to the evaluation criteria. Furthermore, the adaptive methods displayed model robustness in that they worked almost equally well, regardless of the number of factors used in the structural model. Efficiencies of the best adaptive WSR methods approached and even exceeded 100% improvements over OLS regression in beta weight stability and expected predicted mean squared errors. The results tend to support previous findings about WSR methods, but extend generalizations to situations where contamination is present.