I fit a multilevel SEM with cross-level interaction effects with Bayesian MCMC estimation method. The model fits just fine. The problem is with plotting the interaction effects, which are of substantive interest.
My understanding is that I can't plot the marginal effects (Z*X on Y) within Mplus. I wonder though, whether I might be able to get the output of the posterior distributions for covariance matrix (for X Y and Z) and plot the interaction effects in R or Stata?
I would definitely appreciate your insight on this.
I assume that z is a level 2 variable and y and x level 1 variables. You can get the covariance matrix for z and the between part variation of y (and x) and you can get the covariance matrix of the within part of y (and x) - all by doing a fully saturated model.
But isn't it easier to express the interaction effect you want in Model Constraint, say
New(yest); yest = (gamma0 + gamma1*z)*x;
where z moderates the effect of x on y and where, conditioning on z and x, you choose different values of z (say high, middle, low) and vary x over its relevant range. This gives you not only the estimated y but also its SE and can then do a 95% CI.
This begins to make sense--thank you once again for the explanation.
Could you please also point me at the more detailed description of the "Model Constraint" procedure you are referring to? I remember using it before to assess the indirect effects, which is somewhat different from what I want to do now.
Particularly, it's not clear to me how exactly I manipulate the value of z (between-level predictor) in the Model Constraint statement. I assume I can not just type the value of z I want to use (e.g. mean z) in the statement.