Robust Estimation of Structural Equation Modeling using Mahalanobis Distance-based Trimming: An Application to Job Performance Data

Structural Equation Modeling (SEM) is a commonly used and prevalent method to describe the relationships between latent and observed variables. If these variables contain outliers and leverage-points, the estimation by existing SEM is problematic and leads to biased and inefficient estimators. In this article, we propose the Least Mahalanobis Distance-based Trimmed (LMDT) model which uses Mahalanobis distance for the identification of outliers in SEM and trimming approach for dealing with such types of influential observations. By using this suggested technique, instead of maximum likelihood and least squares criteria, the LMDT is resistant to outliers in both measurement error and latent factors. A FAST-iterative algorithm is constructed and implemented for computing the LMDT. Both a simulation study and a real data analysis indicate that the proposed robust method has good performance in terms of bias and efficiency on contaminated and non-normal skewed data and it outperforms the two non-robust and one robust existing estimation methods.