The Effect of Between Group Dependence on Measurement Equivalence/Invariance Tests

Abstract

When using structural equation modeling methods, researchers should test for the presence of measurement equivalence/invariance (ME/I) before investigating substantive hypotheses (Bollen, 1989, p. 355). This study evaluated the robustness of the most common form of ME/I, metric invariance tests using multigroup confirmatory factor analyses, to violations of the independent groups assumption. Based on the analytically derived effect of such a violation on the likelihood ratio test, Jones-Farmer (2010) concluded that the results of the test would be unaffected. A Monte Carlo simulation was conducted to test her hypothesis and evaluate the robustness of other previously suggested ME/I tests that use CFI, SRMR, and RMSEA (Chen, 2007). As part of the study, the effect of among-groups dependence on the parameter estimates of factor loadings and their standard errors was also investigated. Among-groups dependence was found to have no practically significant effect on the results of the likelihood ratio test or the factor loading parameter estimates and standard errors, but other ME/I tests were impacted to varying degrees.