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

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1.5 Model Modification

In application of SEM one usually specifies a model based on theory or empirical findings then fit the model to the available data. Very often the tentative initial model may not fit data well. In other words, the initial model may be somewhat mis-specified. In such a case, the possible sources of lack of model fit need to be assessed to determine what is specifically wrong with the model specification, then modify the model and re-test it using the same data. This process is called ‘model specification search.’

To improve the initial model that does not fit the data satisfactorily, most often the modification indices (MIs) (Sörbom, 1989) that are associated with the fixed parameters of the model are used as diagnostic statistics to capture model mis-specfication. A MI indicates the decrease in model img statistic with 1 df indicating if a particular parameter is freed from a constraint in the preceding model.

A high MI value indicates the corresponding fixed parameter should be freed to improve model fit. Although a drop in img of 3.84 with 1 df indicates a significant model fit improvement at P = 0.05 level, no strict rules of thumb exist concerning how large MIs must be to warrant a meaningful model modification. In Mplus output MIs are listed by default if a drop ...

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