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

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5.2 Multi-Group SEM model

In the last section, we have demonstrated how to test factorial invariance across groups using multi-group CFA model. Very often, invariance of path coefficients is of interest, and we wonder whether some relationships among variables, including observed and unobserved latent variables/factors remain unchanged in different populations or groups, then multi-group SEM applies. In this section we switch our attention to examining invariance of specific structural path coefficients across groups using multi-group SEM. Similar to the multi-group CFA model, some path coefficients in a multi-group SEM model can be restricted to be equal, while other coefficients remain varying, across groups. By testing equality or invariance of path coefficients across groups, it enables us to examine whether different groups behave similarly (Hayduk, 1987).

Our demonstration of the multi-group SEM model will be based on the model specified in Figure 3.4. As discussed in Section 3.2, the relationship between substance abuse and mental health is complicated. For the purpose of model demonstration, we assume: (1) only crack-cocaine use affects mental problems and there are no reciprocal effects; and (2) depression is a function of anxiety, instead of the other way around.

We start by establishing a baseline SEM model for Ohio and Kentucky, respectively. If the baseline models fit data well, we will test: (1) whether the effect of anxiety (ANX, ) on depression (DEP, ) remains unchanged ...

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