A Corrected Goodness-of-Fit Index (CGFI) for Model Evaluation in Structural Equation Modeling

We propose a Corrected Goodness-of-Fit Index (CGFI) for model evaluation in Structural Equation Modeling (SEM). The CGFI is essentially a corrected index that takes into account model complexity and downward bias caused by small sample size. Using simulations based on pre-set SEM models, we compared the properties of CGFI, Goodness-of-Fit (GFI), and Adjusted Goodness-of-Fit Index (AGFI) under different settings of sample size, estimation method, magnitude of factor loadings, model complexity, and types and degrees of model misspecification. We find that the CGFI is more stable across different sample sizes and much more sensitive to detect model misspecification than the GFI and AGFI. We recommend a critical value of 0.90 for the proposed CGFI to evaluate the goodness of fit of SEM. Our proposed CGFI is easy to implement and can serve as a useful supplementary fit index to existing ones.