The Impact of Ignoring Cross-loadings on the Sensitivity of Fit Measures in Measurement Invariance Testing

Abstract

Cross-loadings are common in multiple-factor confirmatory factor analysis (CFA) but often ignored in measurement invariance testing. This study examined the impact of ignoring cross-loadings on the sensitivity of fit measures (CFI, RMSEA, SRMR, SRMRu, AIC, BIC, SaBIC, LRT) to measurement noninvariance. The manipulated design factors included the magnitude and percentage of cross-loadings, the magnitude and percentage of noninvariance, location of measurement noninvariance, model size, and sample size. Results suggested that the ignored cross-loadings affected the sensitivity of all fit measures but LRT to metric noninvariance to varying degrees, whereas they did not affect the sensitivity of fit measures to scalar noninvariance except for RMSEA. RMSEA was impacted by the magnitude of cross-loadings in both metric and scalar invariance testing. In the largest model size, CFI failed to detect metric noninvariance when there were no cross-loadings in the population model but detected the metric noninvariance of .30 with ignored cross-loadings.