Abstract: There are some limitations in the commonly used fit indices of structural equation model. For example, χ², which is set up to reject the traditional null hypothesis, cannot be used to endorse a model, while descriptive fit indices such as RMSEA and CFI do not have inferential statistical properties. Equivalence testing can effectively compensate for the limitations mentioned above. In this paper, the way to use equivalence testing in evaluating the fit of a single model and its difference from the null hypothesis testing were introduced first. Then the approach to analyze measurement invariance by equivalence testing was described. Furthermore, empirical data was used to demonstrate the effectiveness of equivalence testing in single model evaluation and measurement invariance test, and to compare equivalence testing with traditional model evaluation method.

Key words: structural equation model, fit indices, equivalence testing, null hypothesis testing, measurement invariance