Assessing Structural Equation Models by Equivalence Testing With Adjusted Fit Indexes

Ke‐Hai Yuan · Wai Chan · George A. Marcoulides · Peter M. Bentler

226 citations0/0 files storedStructural Equation Modeling A Multidisciplinary Journal

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Psychometric Methodologies and Testing Statistical Methods and Applications Statistical Methods and Bayesian Inference

Abstract

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.

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1999Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives 1992Alternative Ways of Assessing Model Fit 1990Comparative fit indexes in structural models.1998Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification.1996Power analysis and determination of sample size for covariance structure modeling.1989EQS : structural equations program manual 1989LISREL 7 : user's reference guide 1989A New Incremental Fit Index for General Structural Equation Models

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2017Evaluating the metacognitive awareness inventory using empirical factor-structure evidence 2016New Ways to Evaluate Goodness of Fit: A Note on Using Equivalence Testing to Assess Structural Equation Models 2020The Poor Fit of Model Fit for Selecting Number of Factors in Exploratory Factor Analysis for Scale Evaluation 2020“How Well Does Your Structural Equation Model Fit Your Data?”: Is Marcoulides and Yuan’s Equivalence Test the Answer?2018Comparing Exploratory Structural Equation Modeling and Existing Approaches for Multiple Regression with Latent Variables

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