A monte carlo approach for nested model comparisons in structural equation modeling

Abstract

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.