A simulation study to investigate the use of cutoff values for assessing model fit in covariance structure models

In this paper, we used simulations to investigate the effect of sample size, number of indicators, factor loadings, and factor correlations on frequencies of the acceptance/rejection of models (true and misspecified) when selected goodness-of-fit indices were compared with prespecified cutoff values. We found the percent of true models accepted when a goodness-of-fit index was compared with a prespecified cutoff value was affected by the interaction of the sample size and the total number of indicators. In addition, for the Tucker-Lewis index (TLI) and the relative noncentrality index (RNI), model acceptance percentages were affected by the interaction of sample size and size of factor loadings. For misspecified models, model acceptance percentages were affected by the interaction of the number of indicators and the degree of model misspecification. This suggests that researchers should use caution in using cutoff values for evaluating model fit. However, the study suggests that researchers who prefer to use prespecified cutoff values should use TLI, RNI, NNCP, and root-mean-square-error-of-approximation (RMSEA) to assess model fit. The use of GFI should be discouraged.