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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. [ABSTRACT FROM AUTHOR]

Model size has been shown to influence model fit measures in structural equation modeling, whereas its impact on measurement invariance testing using recommended cutoff criteria of fit measures is not clear. This study examined the impact of model size on the sensitivity of fit measures (CFI, RMSEA, AIC, BIC, SaBIC, LRT) to measurement noninvariance. Results suggested that CFI and RMSEA failed to detect metric noninvariance when model size was large (e.g., 6 factors with 8 items per factor). AIC and LRT were minimally affected by model size. Recommendations for empirical researchers were provided based on the findings of this simulation study. [ABSTRACT FROM AUTHOR]

Exploratory structural equation modeling (ESEM) allows for the estimation of all cross-loadings, which leads to the number of parameters estimated substantially greater than that in conventional SEM. This study examined the sensitivity of fit measures (CFI, RMSEA, AIC, BIC, SaBIC, LRT) to measurement noninvariance in ESEM. Results suggested that the sensitivity of the fit measures depended on the magnitude of noninvariance, model complexity, and sample size. The sensitivity of LRT to both metric and scalar noninvariance was high. Comparative fit index tended to filter out small noninvariance with large sample sizes. Root mean squared error of approximation failed to detect even a large measurement noninvariance when the model was complex and sample size was below 300 per group. Information criteria were more sensitive to scalar noninvariance than to metric noninvariance. Implications and recommendations based on the findings were discussed. [ABSTRACT FROM AUTHOR]