Evaluating SEM Model Fit with Small Degrees of Freedom

Research has revealed that the performance of root mean square error of approximation (RMSEA) in assessing structural equation models with small degrees of freedom (df) is suboptimal, often resulting in the rejection of correctly specified or closely fitted models. This study investigates the performance of standardized root mean square residual (SRMR) and comparative fit index (CFI) in small df models with various levels of factor loadings, sample sizes, and model misspecifications. We find that, in comparison with RMSEA, population SRMR and CFI are less susceptible to the effects of df. In small df models, the sample SRMR and CFI could provide more useful information to differentiate models with various levels of misfit. The confidence intervals and p-values of a close fit were generally accurate for all three fit indices. We recommend researchers use caution when interpreting RMSEA for models with small df and to rely more on SRMR and CFI.