The Performance of Equivalence-Based Fit Indices with Bootstrapped Confidence Intervals and Varied Tolerable Cutoffs

This study examines equivalence testing for assessing model fit in structural equation modeling (SEM). Equivalence testing evaluates whether model misspecification is sufficiently small to be considered tolerable rather than testing for exact model fit. Using a Monte Carlo simulation, this study evaluates equivalence testing procedures incorporating bootstrapped confidence intervals and alternative cutoff values for SEM fit indices, providing empirical guidance for researchers evaluating model fit in SEM. Based on the results, sample sizes of 400 or greater are generally recommended for the examined equivalence-based tests to perform optimally across examined conditions. The bootstrapped equivalence-based CFI with a cutoff of .95 performed most optimally in the current study followed closely by the bootstrapped original SRMR with a cutoff of .05. The results suggest using these two indices in conjunction to balance endorsement of tolerably misspecified models and reserving endorsement of intolerably misspecified models.