I am running a complicated SEM in two stages (it is too computationally intensive to run in a single analysis). The first stage involves 3 latent variables, with Y regressed on X and Z; all three are latent variables with observed indicators. X and Z interact. In the second model, X and Z are regressed on each other, with observed covariates to identify the model. So it looks like this:
Model 1: Y on Z X intZX
Model 2 (omitting identifying covariates): Z on X X on Z
I would like to compare the magnitude of X and Z's effect on Y. This would usually be simple, and could be done just by fixing the variance of each to 1. However because they are both DVs in another model, I don't think this will work. My understanding is that X@1 statements would then fix the residual variance (i.e. the unexplained portion of the variance), rather than the total variance. Is that correct? Is there a simple way to set these latent variables to have the same scale that works whether they are IVs or DVs?