The Robustness of ME/I Evaluations to Among-Group Dependence

Abstract

This study evaluates the robustness of multisample confirmatory factor analysis approaches to measurement equivalence/invariance (ME/I) evaluations under a specific model misspecification: when independence among the groups is assumed, but groups are dependent. Monte Carlo simulation is used to investigate the robustness of several ME/I evaluation procedures including the likelihood ratio test (), ΔCFI, ΔSRMR, and ΔRMSEA. The effect of this model misspecification on the factor loadings and their standard errors is also considered. Assuming the groups are independent when they are not is shown to have no practical effect on the results of the , ΔCFI, ΔSRMR, or ΔRMSEA procedures because the effect of model misspecification is canceled out through differencing. Similarly, the estimated factor loadings and standard errors are not significantly affected by incorrectly assuming among-group dependence. These results are used to develop recommendations for researchers who conduct multigroup analyses using structural equation models with samples in which independence is unclear.

Keywords:

• confirmatory factor analysis
• measurement invariance
• multigroup SEM

Notes

¹ It is important to note that the decision rules based on the fit indices other than Δχ² are not true hypothesis tests, thus the terms Type I and Type II error are used loosely when referring to other ME/I procedures. The decision rules for ΔCFI, ΔRMSEA, and ΔSRMR are the recommendations of Chen (2007) based on his investigation of the empirical sampling distributions of these fit indexes.

²The full simulation results can be obtained from the first author.