The effect of model misspecification on overall goodness-of-fit indices for structural equation modeling

The purpose of the present study was to investigate empirically the sensitivity of 12 commonly used SEM fit indices derived from ML estimation method to degree and type of model misspecification under different sample size conditions. Moreover, the study evaluated the efficacy of cutoff score currently used as criteria for assessing model fit. A modified version of a published nonrecursive SEM model was used in the study as the population model. The performance of fit indices was examined over five levels of model misspecification (ranged from no error to extensive misspecification), two types of model misspecification (recursive and nonrecursive misspecification) and five levels of sample size (ranged from 100 to 2000). A three-factor balanced design was used in the present study with repeated measures over degree and type of misspecification. Data were generated using EQS 6 under different model misspecifications/sample size conditions. Findings from this study showed that the goodness-of-fit test did not equally detect the same size of error in different types of models. Fit indices were less sensitive to recursive than nonrecursive misspecification under the same size of sample and misspecification conditions. Therefore, conclusions on whether there is a misspecification in the model greatly differ with the size and type of specification error in the model as well as the size of sample. Fit indices were greatly varied in their reliability of estimation and sensitivity to sample size. IFI, NNFI, RNI and CFI, RMSEA and MCI were the fit indices that showed the highest reliability and lowest sensitivity to sample size among all fit indices studied. Moreover, results of the present study showed that RMSEA tends to slightly overreject true-population model under small sample size (e.g., N ≤ 200). Using the ability of indices to discriminate between true and misspecified models (Hu & Bentler, 1998; 1999), the following cutoff scores were recommended: MCI with a cutoff score of .94, IFI, RNI, and CFI with a cutoff score of .97, RMSEA with a cutoff score of .06 and NNFI with a cutoff score of .93.