We need to change how we compute RMSEA for nested model comparisons in structural equation modeling.

Comparison of nested models is common in applications of structural equation modeling (SEM). When two models are nested, model comparison can be done via a chi-square difference test or by comparing indices of approximate fit. The advantage of fit indices is that they permit some amount of misspecification in the additional constraints imposed on the model, which is a more realistic scenario.

Type I error rates and power of several versions of scaled chi-square difference tests in investigations of measurement invariance.

A Monte Carlo simulation study was conducted to investigate Type I error rates and power of several corrections for nonnormality to the normal theory chi-square difference test in the context of evaluating measurement invariance via structural equation modeling. Studied statistics include the uncorrected difference test, , Satorra and Bentler's (2001) original correction, , Satorra and Bentler's (2010) strictly positive correction, , and a hybrid procedure, (Asparouhov & Muthén, 2013). Multiple-group data were generated from confirmatory factor analytic population models invariant on all parameters, or lacking invariance on residual variances, indicator intercepts, or factor loadings.