Assessing Structural Equation Models by Equivalence Testing With Adjusted Fit Indexes

By Ke-Hai Yuan, Wai-Sum Chan, George A. Marcoulides, Peter M. Bentler. 2016

209 citations recorded by the source corpus.

Conventional null hypothesis testing (NHT) is a very important tool if the ultimate goal is to find a difference or to reject a model. However, the purpose of structural equation modeling (SEM) is to identify a model and use it to account for the relationship among substantive variables. With the setup of NHT, a nonsignificant test statistic does not necessarily imply that the model is correctly specified or the size of misspecification is properly controlled. To overcome this problem, this article proposes to replace NHT by equivalence testing, the goal of which is to endorse a model under a null hypothesis rather than to reject it. Differences and similarities between equivalence testing and NHT are discussed, and new “T-size” terminology is introduced to convey the goodness of the current model under equivalence testing. Adjusted cutoff values of root mean square error of approximation (RMSEA) and comparative fit index (CFI) corresponding to those conventionally used in the literature are obtained to facilitate the understanding of T-size RMSEA and CFI. The single most notable property of equivalence testing is that it allows a researcher to confidently claim that the size of misspecification in the current model is below the T-size RMSEA or CFI, which gives SEM a desirable property to be a scientific methodology. R code for conducting equivalence testing is provided in an appendix.

Subfields: Computer Networks and Communications, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/3578fa9e2fb52c719d66b4c0fcdcfb9ce7a2d94f

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In Computer Networks and Communications

In Management Science and Operations Research

Citations in the corpus

New Ways to Evaluate Goodness of Fit: A Note on Using Equivalence Testing to Assess Structural Equation Models (2017, methodology): “Currently there appears to be a growing consensus in the literature that goodness of fit is most appropriately assessed using a variety of different perspectives (Yuan et al., 2016).”
Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression with Latent Variables (2018, background): “In our case given sample size N ¼ 200, RMSEAt<:085 and CFIt>:890 are considered to be good for SEM; while for ESEM the corresponding criteria are RMSEAt<:082 and CFIt>:891 (see calculation in Yuan et al., 2016).”
Testing Factorial Invariance With Unbalanced Samples (2018, background): “Readers can consult Yuan and Chan (2016) and Yuan et al. (2016) for more detailed discussions.”
Examination of the Weighted Root Mean Square Residual: Evidence for Trustworthiness? (2018, methodology): “However, most prior studies involving ad hoc fit idexes have conducted investigations in a similar manner (Yuan et al., 2016).”
Evaluating the metacognitive awareness inventory using empirical factor-structure evidence (2018, background): “On these, a value of 1.00 suggests that there is a perfect fit and values above .95 are commonly interpreted to mean that the model-data fit is good (Hu and Bentler 1999; cf., Yuan et al. 2016).”