A Note on Comparing Equivalence Testing with Conventional Criteria in Evaluating the Overall Fit of Structural Equation Models

This research note considers equivalence testing strategies relative to conventional criteria commonly used for the evaluation of model fit in structural equation modeling. The comparison is conducted in light of recent calls by some researchers to abandon the use of the equivalence testing approach. The primary emphasis of the current study is on evaluating published results and recommendations in order to determine whether they accurately reflect the performance of the equivalence testing approach. We demonstrate that the overall message of recent works is mostly from a lack of a coherent understanding and implementation of the equivalence testing approach. We explicate specific details about the approach to facilitate proper interpretation of the reported results.