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Fit indexes were compared with respect to a specific type of model misspecification. Simple structure was violated with some secondary loadings that were present in the true models that were not specified in the estimated models. The c2 test, Comparative Fit Index, Goodness-of-Fit Index, Incremental Fit Index, Nonnormed Fit Index, root mean squared error of approximation, standardized root mean square residual, and the c2/df values were investigated. Simulated data sets with 3 sample sizes (250, 500, and 1,000 cases), 4 levels of main loadings (.40,. 50,. 60, and. 80), 2 numbers of factors (4, 8), and 2 types of association matrix (covariance, correlation) were the basis for maximum likelihood estimation of orthogonal and oblique factor models. Some correlations between fit indexes were low. Moreover, small distortions from simple structure did not lead to misfit in the RMSEA and SRMR, but they often led to misfit in the incremental fit indexes. This result may be of interest for research on personality traits, where small violations of simple structure are very common.
Beauducel et al. (Sat,) studied this question.