Using ΔGoodness-of-Fit Indexes in Assessing Mean Structure Invariance

In research concerning model invariance across populations, researchers have discussed the limitations of the conventional χ2 difference test (Δχ2 test). There have been some research efforts in using goodness-of-fit indexes (i.e., δgoodness-of-fit indexes) for assessing multisample model invariance, and some specific recommendations have been made (Cheung & Rensvold, 2002 Cheung, G. W. and Rensvold, R. B. 2002. Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 9: 233–255. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Because δgoodness-of-fit indexes were designed to assess model fit in terms of covariance structure, it is not clear how they will perform when mean structure invariance is the research focus. This study extends the previous work (Cheung & Rensvold, 2002 Cheung, G. W. and Rensvold, R. B. 2002. Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 9: 233–255. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and evaluates how δgoodness-of-fit indexes perform in mean structure invariance analysis. By using a Monte Carlo simulation experiment, the performance of δgoodness-of-fit indexes in detecting population mean structure difference is evaluated. The findings suggest that, in general, δgoodness-of-fit indexes are so sensitive to model size that they are not generally useful in mean structure invariance analysis.