"How Well Does Your Structural Equation Model Fit Your Data?": Is Marcoulides and Yuan's Equivalence Test the Answer?

Structural equation modeling is an ideal data analytical tool for testing complex relationships among many analytical variables. It can simultaneously test multiple mediating and moderating relationships, estimate latent variables on the basis of related measures, and address practical issues such as nonnormality and missing data. To test the extent to which a hypothesized model provides an appropriate characterization of the collective relationships among its variables, researchers must assess the "fit" between the model and the sample's data. However, interpreting estimates of model fit is a problematic process. The traditional inferential test of model fit, the chi-square test, is biased due to sample size. Fit indices provide descriptive (i.e., noninferential) values of model fit (e.g., comparative fit index, root-mean-square error of approximation), but are unable to provide a definitive "acceptable" or "unacceptable" fit determination. Marcoulides and Yuan have introduced an equivalence-testing technique for assessing model fit that combines traditional descriptive fit indices with an inferential testing strategy in the form of confidence intervals to facilitate more definitive fit conclusions. In this paper, we explain this technique and demonstrate its application, highlighting the substantial advantages it offers the life sciences education community for drawing robust conclusions from structural equation models. A structural equation model and data set (N = 1902) drawn from previously published research are used to illustrate how to perform and interpret an equivalence test of model fit using Marcoulides and Yuan's approach.