Evaluating the Fit of Structural Equation Models

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Structural equation modeling (SEM) has been increasingly recognized as a useful quantitative method in testing hypothesized theoretical models that are substantively meaningful in the real world. To evaluate the degree of fit of a SEM model, several measures of fit, so-called fit indices are normally used. A fit index is an overall summary statistic that evaluates how well a particular SEM model explains the sample data. The use of fit indices as measures of model fit became very popular with time, however, none of which has been endorsed as the "best index" by the majority of researchers. This situation put applied researchers in a real challenge in selecting appropriate fit indices among the large number of fit indices available in many popular SEM programs. This work 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 scores currently used as criteria for assessing model fit and some recommendations for practitioners are given.