A Monte Carlo Approach for Nested Model Comparisons in Structural Equation Modeling
This paper proposes a Monte Carlo approach for nested model comparisons. This approach allows for test of approximate equivalency in fit between nested models and customizing cutoff criteria for difference in a fit index. Different methods to account for trivial misspecification in the Monte Carlo approach are also discussed. A simulation study is conducted to compare the Monte Carlo approach with different methods of imposing trivial misspecification to chi-square difference test and change in comparative fit index (CFI) with suggested cutoffs. The simulation study shows that the Monte Carlo approach is superior to the chi-square difference test by correctly retaining the nested model with trivial misspecification. It is also superior to the change in CFI by offering higher power to detect severe misspecification.
KeywordsRejection Rate Nest Model Target Model Monte Carlo Approach Data Generation Model
Partial support for this project was provided by grant NSF 1053160 (Wei Wu & Todd D. Little, co-PIs) and by the Center for Research Methods and Data Analysis at the University of Kansas (when Todd D. Little was director). Todd D. Little is now director of the Institute for Measurement, Methodology, Analysis, and Policy at Texas Tech University. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the funding agencies.
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