Dear friend Tarek Fayed
The Chow test is a statistical test used to determine if there is a structural break in a time series regression. While there is no exact equivalent of the Chow test in SEM (Structural Equation Modeling), there are similar tests that can be used to assess the significance of differences in model parameters across groups or time points.
One such test is the multiple-group analysis or multi-group SEM, which compares the fit of two or more models with different parameter estimates to test for differences in the relationships among the latent variables between the groups. Another test is the cross-lagged panel model, which tests for reciprocal causation between two or more variables at different time points.
In summary, there is no direct equivalent of the Chow test in SEM, but there are similar tests available to evaluate differences in model parameters between groups or time points.
Hi Tarek
You might want to consider piecewise growth models - an extension (or submodel) of the general growth curve model that can be specified and fitted in a SEM framework. This could be used to test for differences in linear trend across time by incorporating two (or more) slopes. As Kaushik mentioned a multigroup model could also be used to compare slopes across groups, or even piecewise models could be compared across groups.
Mark
Article Modeling Growth in Latent Variables Using a Piecewise Function
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