Li‐tze Hu

This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and Gamma Hat; a cutoff value close to .90 for Mc; a cutoff value close to .08 for SRMR; and a cutoff value close to .06 for RMSEA are needed before we can conclude that there is a relatively good fit between the hypothesized model and the observed data. Furthermore, the 2‐index presentation strategy is required to reject reasonable proportions of various types of true‐population and misspecified models. Finally, using the proposed cutoff criteria, the ML‐based TLI, Mc, and RMSEA tend to overreject true‐population models at small sample size and thus are less preferable when sample size is small.

This study evaluated the sensitivity of maximum likelihood (ML)-, generalized least squares (GLS)-, and asymptotic distribution-free (ADF)-based fit indices to model misspecification, under conditions that varied sample size and distribution. The effect of violating assumptions of asymptotic robustness theory also was ex-amined. Standardized root-mean-square residual (SRMR) was the most sensitive index to models with misspecified factor covariance(s), and Tucker-Lewis Index (1973; TLI), Bollen's fit index (1989; BL89), relative noncentrality index (RNI), comparative fit index (CFI), and the ML- and GLS-based gamma hat, McDonald's centrality index (1989; Me), and root-mean-square error of approximation (RMSEA) were the most sensitive indices to models with misspecified factor loadings. With ML and GLS methods, we recommend the use of SRMR, supple-mented by TLI, BL89, RNI, CFI, gamma hat, Me, or RMSEA (TLI, Me, and RMSEA are less preferable at small sample sizes). With the ADF method, we recommend the use of SRMR, supplemented by TLI, BL89, RNI, or CFI. Finally, most of the ML-based fit indices outperformed those obtained from GLS and ADF