Fit Index Criteria for Multisample SEM with Ordinal Data

• In Event: Beyond Traditional SEM: Model Fit, Heterogeneity, and New Paradigms

Abstract

Reliable group comparisons in structural equation modeling (SEM) rest on measurement invariance, yet fit index cut offs derived from continuous data often misfire with ordinal indicators. We gauged the diagnostic accuracy of ΔCFI, ΔRMSEA, and ΔSRMR via Monte Carlo simulations that varied sample size (200, 400, 1,000), group size ratio (1:1 vs. 1:2), model complexity, latent response distribution, Likert format (3 , 5 , 7 point), and noninvariance pattern (metric vs. scalar; bias magnitude and proportion). Using robust estimators (ML SB, WLSMV) and ROC analysis, ΔCFI and ΔRMSEA outperformed ΔSRMR—especially for scalar noninvariance—yet required stricter cut offs (< 0.01 CFI; < 0.015 RMSEA). ΔSRMR showed inflated false positive rates and low power, underscoring the need for context specific thresholds and robust estimation.

Authors

• Suat Babayigit, University of Miami

• Stephen A. Sivo, University of Central Florida