Evaluating the Performance of Existing and Novel Equivalence Tests for Structural Equation Modeling

It has been suggested that equivalence testing (otherwise known as negligible effect testing) be used to evaluate model fit within structural equation modeling (SEM). This dissertation is composed of two studies that propose novel equivalence tests based on the popular RMSEA, CFI and SRMR fit indices. Using Monte Carlo simulations, each study compares the performance of these novel tests to other existing equivalence testing-based fit indices in SEM, as well as to other methods commonly used to evaluate model fit. In each study, results indicate that equivalence tests in SEM have good Type I error control and display considerable power for detecting well-fitting models in medium to large sample sizes. At small sample sizes, relative to traditional fit indices, equivalence tests limit the chance of supporting a poorly fitting model. Both studies also present illustrative examples to demonstrate how equivalence tests can be incorporated in model fit reporting. We recommend that equivalence tests be utilized in conjunction with descriptive fit indices to provide more evidence when evaluating model fit.