Effect Sizes of Model Misfit in Structural Equation Models

Residual correlations and covariances provide effect sizes of the misfit of covariance structure models. In a simulation study, we found that accurate confidence intervals (CIs) for standardized residual covariances are obtained even in small samples (N = 100), regardless of model size, degree of model misspecification, and data distribution. Standardized residual covariances also provide information about the source of misfit in poorly fitting models. From this viewpoint, they may be considered an alternative to modification indices. We compared the empirical Type I errors and power rates of standardized residual covariances and modification indices and found that both procedures provide nearly identical rates across the simulation conditions investigated. Residual correlations and standardized residual covariances provide very similar results.