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. The most popular index of approximate fit is the root mean square error of approximation (RMSEA). In this article, we argue that the dominant way of comparing RMSEA values for two nested models, which is simply taking their difference, is problematic and will often mask misfit. We instead advocate computing the RMSEA associated with the chi-square difference test. We are not the first to propose this idea, and we review numerous methodological articles that have suggested it. Nonetheless, these articles appear to have had little impact on actual practice. The modification of current practice that we call for may be particularly needed in the context of measurement invariance assessment. We illustrate the difference between the current approach and our advocated approach on three examples, where two involve multiple-group and longitudinal measurement invariance assessment and the third involves comparisons of models with different numbers of factors. We conclude with a discussion of limitations and future research directions.
We need to change how we compute RMSEA for nested model comparisons in structural equation modeling