Understanding Robust Corrections in Structural Equation Modeling

Robust corrections to standard errors and test statistics have wide applications in structural equation modeling (SEM). The original SEM development, due to Satorra and Bentler (1988, 1994), was to account for the effect of nonnormality. Muthen (1993) proposed corrections to accompany certain categorical data estimators, such as cat-LS or cat-DWLS. Other applications of robust corrections exist. Despite the diversity of applications, all robust corrections are constructed using the same underlying rationale: They correct for inefficiency of the chosen estimator. The goal of this article is to make the formulas behind all types of robust corrections more intuitive. This is accomplished by building an analogy with similar equations in linear regression and then by reformulating the SEM model as a nonlinear regression model.