I am testing a multilevel structural equation model with a 3-wave longitudinal dataset. I have nested all three measurements within individuals and all the paths I am interested in include within-level variables. I would now like to perform group analysis to my data. So I would like to see if the coefficients are different between group 1 and group 2 of the sample. The problem is that the grouping variable is also a within-level variable and is changing over time. So its value can be either 1 or 2 across times 1-3. How can I do that with Mplus?
The reason why I need to do that is because I am using an incogruence score between A and B (both within-level variables) as a predictor in my model. I am more interested in the incogruence than the interaction between the two variables. But in order to address criticisms around the use of incogruence scores, I would need to perform my analyses for two groups: Group 1: A > B and Group 2: A < B.
If I use the grouping variable as a dummy time-varying covariate, I will control for its effect, but I will still not be able to compare the results between group 1 and group 2.
The only way to do that is to create an interaction between my incogruence score and the covariate? But this is too complicated and I am not sure what that variable would mean. Then it would be better to use an interaction term all the way from the start, right?