Further understanding of fit indices in evaluating model fit of structural equation models

A simulation of over one million samples from over 5,000 population parameters was conducted to examine the performance of fit indices and conventional rules of thumb in evaluating model fit of structural equation models. Results suggest that since values of fit indices were affected by sample sizes, model complexity and measurement errors, conventional rules that recommend a single cutoff value for all models is inappropriate. Moreover, recently some structural equation modeling programs (such as LISREL) report fit indices derived from the normal theory weighted least squares fÓ2 (C2) while the conventional rules were developed for fit indices derived from maximum likelihood fÓ2 (C1). Our simulation finds that using conventional rules but C2-based fit indices may not have enough power to reject misspecified models. Finally, results show that some fit indices are more sensitive to missing cross-loadings while others are more sensitive to missing structural paths. Hence, we recommend a two-index strategy, using standardized root-mean-square residual (SRMR) and Gamma Hat, with corresponding cutoff values at various sample sizes, number of factors, and number of items per factor to evaluate model fit.