Sensitivity of Fit Indices to Model Misspecification and Model Types

The search for cut-off criteria of fit indices for model fit evaluation (e.g., Hu & Bentler, 1999 Hu, L. and Bentler, P. M. 1999. Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling., 6: 1–55. Taylor & Francis Online, Web of Science ® , Google Scholar) assumes that these fit indices are sensitive to model misspecification, but not to different types of models. If fit indices were sensitive to different types of models that are misspecified to the same degree, it would be very difficult to establish cut-off criteria that would be generally useful. The issue about SEM fit indices being sensitive to different types of models has not received sufficient attention, although there is some research suggesting that this might be the case (e.g., Kenny & McCoach, 2003 Kenny, D. A. and McCoach, D. B. 2003. Effect of the number of variables on measures of fit in structural equation modeling. Structural Equation Modeling., 10: 333–351. Taylor & Francis Online, Web of Science ® , Google Scholar). This study examines if fit indices are sensitive to different types of models while controlling for the severity of model misspecification. The findings show that most fit indices, including some very popular ones (e.g., RMSEA), may be sensitive to different types of models that have the same degree of specification error. The findings suggest that, for most fit indices, it would be difficult to establish cut-off criteria that would be generally useful in SEM applications.