Abstract

This study aims to comprehensively examine the characteristics and limitations of various indices applicable to non-nested model selection in structural equation modeling (SEM). Monte Carlo simulations were conducted using fit indices (CFI, TLI, RMSEA, SRMR), the information-based index (ΔBIC), and the Vuong test. The simulation design employed a 3×3×3×4 factorial structure varying factor loading differences, error correlations, factor correlations, and sample sizes, yielding 108 conditions with 1,000 replications each. The findings indicate that CFI and TLI were particularly sensitive to structural misspecifications and demonstrated stable discriminative power with larger sample sizes. In contrast, RMSEA was substantially influenced by sample size and degrees of freedom, tending to impose stricter thresholds, while SRMR showed limitations in distinguishing models when factor correlations were high. BIC provided a quantitative measure of model differences but was constrained in interpretation under equal degrees of freedom. The Vuong test supplemented BIC by offering statistical significance, thereby reinforcing the basis for model selection. Overall, this study provides practical recommendations for comparison strategies, emphasizing that researchers should avoid reliance on a single index and instead adopt complementary interpretations across indices to achieve more robust and reliable model selection.