Assessing Cutoff Values of SEM Fit Indices: Advantages of the Unbiased SRMR Index and Its Cutoff Criterion Based on Communality

Holding model misspecification constant, the behavior of fit indices depends on factors such as the number of variables being modeled (model size), and the average observed correlation (magnitude of factor loadings or measurement quality). We examine by simulation the interplay of these factors with sample size in CFA models. When a biased estimator of the fit index is used (CFI, TLI, or GFI), the behavior of the sample indices depends on sample size, rendering establishing cutoff values impossible. When an unbiased estimator is used (SRMR, or RMSEA) the behavior of the indices matches that of the population parameter and depends on the average R-2 of the observed variables (communality); and for the RMSEA, also on model size. The use of the unbiased SRMR with a cutoff value adjusted by R-2 is recommended as it enables assessing the degree of a model misspecification across model size, sample size, and measurement quality.

Automated summary

The behavior of fit indices in CFA models depends on factors such as model size, sample size, and measurement quality. Biased estimators of fit indices result in unstable behavior with changing sample size, making it difficult to establish cutoff values. Unbiased estimators, on the other hand, match the behavior of population parameters and depend on the average R-2 of observed variables and model size.