Using Equivalence Testing to Evaluate Goodness of Fit in Multilevel Structural Equation Models

Multilevel structural equation models (MSEM) are typically evaluated on the basis of goodness of fit indices. A problem with these indices is that they pertain to the entire model, reflecting simultaneously the degree of fit for all levels in the model. Consequently, in cases that lack model fit, it is unclear which level model is misspecified. Although some researchers have suggested that model fit be assessed separately at all levels, this is not always ideal as it depends on the choice of fit indices, cutoff points, and magnitude of the intraclass correlation. Equivalence testing has recently been recommended as a superior way to evaluate the goodness of fit of models. The approach has also been heralded as a way to advance the inferential nature of structural equation modeling as a confirmatory tool. The purpose of this paper is to illustrate the use of equivalence testing for assessing multilevel model fit in educational research. Although the described procedures can be easily generalized to models with more than two levels, for simplicity we explicitly consider only two-level models.