Fit Index Criteria For Multisample Analysis in SEM with Ordinal Data: A Monte Carlo Simulation Study

Measurement invariance is crucial for valid group comparisons in structural equation modeling (SEM), yet testing invariance becomes challenging when using ordinal data. This dissertation evaluates the adequacy of widely used fit index difference criteria (ΔCFI, ΔRMSEA, ΔSRMR) for multisample invariance testing with ordinal indicators. Traditional Δ fit cutoff thresholds were established based on continuous, normally distributed data, but ordinal measures can distort invariance conclusions. Monte Carlo simulations address this issue by manipulating a comprehensive set of conditions: sample sizes (200, 400, 1000), group size ratios (equal vs. unequal), model complexity (low vs. high), underlying distributions (normal vs. nonnormal), Likert scale formats (3-, 5-, 7-point), and varying measurement noninvariance patterns (metric vs. scalar level, with different proportions and magnitudes of item bias). The simulation employed robust estimation methods (ML with Satorra-Bentler correction and WLSMV), which are appropriate for ordinal data. The findings demonstrated that ΔCFI and ΔRMSEA were more reliable indicators of invariance, particularly for scalar noninvariance. Using empirically derived cutoffs from ROC analysis, both indices showed improved sensitivity and specificity. The optimal thresholds were more stringent than the conventional 0.01 and 0.015 values, indicating that standard criteria may underestimate group differences with ordinal data. In contrast, ΔSRMR proved less reliable: it exhibited inflated false-positive rates across most conditions. It often lacked the power to detect true invariance violations. Fit index performance also depended on study conditions. Smaller samples and mild measurement differences often produced negligible changes in fit indices, whereas large samples made the indices overly sensitive to trivial misfits. Additionally, ΔCFI and ΔRMSEA were more effective in detecting scalar noninvariance, whereas ΔSRMR showed some utility in identifying metric-level differences in simpler models. These results support the use of refined cutoffs and robust estimation methods that account for sample size, distribution, and model complexity to improve measurement invariance testing in SEM.