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Structural Equation Modeling: Applications Using Mplus by Xiaoqian Wang, Jichuan Wang

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1.4 Model Evaluation

A key feature of SEM is to conduct an overall model fit test on the basic hypothesis S = img. That is, to assess the degree to which the model estimated variance/covariance matrix img differs from the observed sample variance/covariance matrix S (Hoelter, 1983; Bollen, 1989a; Jöreskog and Sörbom, 1989; Bentler, 1990). If the model estimated variance/covariance matrix, img, is not statistically different from the observed data covariance matrix, S, then we say the model fits data well, and we accept the null hypothesis or we say the model supports the plausibility of postulated relations among the variables; otherwise the model does not fit the data, and the null hypothesis should be rejected. The overall model fit evaluation should be done before interpreting the parameter estimates. Without evaluating the model fit any conclusion from the model estimation could be misleading.

To assess the closeness of S to img, numerous model fit indices have been developed. For detail information on model fit testing and model fit indices, the readers are referred to Marsh, Balla, and McDonald ...

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