Hello, I'm interested in creating an LGM where I estimate an interaction term between the latent slope variable and an observed covariate in order to predict an outcome variable. Typically, when I create interaction terms I center each variable around its mean so that the coefficients are interpretable. However, I am unsure how to center the slope term around its mean without constraining the model so that there is zero growth. I am also examining an interaction between the same covariate and the latent intercept term in the same model. Can you advise me how to best go about creating this interaction term between the slope and a covariate? Thank you very much for your assistance.
An interaction between an intercept growth factor and a covariate is shown on slides 125-132 in our Topic 3 course handout on this web site. Here the intercept mean is fixed at 0. You are right that the slope mean should not be fixed at zero. I think the interaction can be interpreted even when the slope mean is not zero. The reasoning on slides 131 and 132 can be extended to this case. The term "0.045 - 0.047*i" won't be 0.045 at the i mean if the i mean is not zero, but I don't think that is problematic in the interpretation.