Evaluating Equivalence Testing Methods for Measurement Invariance

Measurement Invariance (MI) is often concluded from a nonsignificant chi-square difference test. Researchers have also proposed using change in goodness of fit indices (∆GOFs) instead. Both of these commonly used methods for testing MI have important limitations. To combat these issues, Yuan and Chan (2016) proposed using an equivalence test (EQ) to replace the chi-square difference test commonly used to test MI. Due to their concerns with the EQ’s power, Yuan and Chan also created an adjusted version (EQ-A), but provide little evaluation of either procedure. The current study evaluated the Type I error and power of both the EQ and EQ-A, and compared their performance to that of the traditional chi-square difference test and ∆GOFs. The EQ for nested model comparisons was the only procedure that always maintained empirical error rates below the nominal alpha level. Results also highlight that the EQ requires larger sample sizes than traditional difference-based approaches or using equivalence bounds based on larger than conventional RMSEA values (e.g., > .05) to ensure adequate power rates. We do not recommend Yuan and Chan’s proposed adjustment (EQ-A) over the EQ.