The Impact of Model Size on the Sensitivity of Fit Measures in Measurement Invariance Testing

Abstract

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.