I am looking to INTERACT two Level 1 variables (1-1) to predict a Level 2 outcome.
In other words, this is 1x1 -> 2 model.
Although Preacher (2011) provides Mplus code for a 1-1-2 MEDIATION model, I am wondering if it is possible to use Mplus to for a 1x1 INTERACTION on a Level 2 variable.
That is, how do I bring that interaction up to the latent level? I do not wish to simply create group averages of the two Level 1 variables, as that would make for a 2 x 2 -> 2 model, and the meaning of the theory / idea I am trying to test would be changed.
I understand that such a bottom-up model is relatively rare and typically challenging from a statistical standpoint, but I am wondering if there is any capability within Mplus to create and reasonably interpret a 1 X 1 -> 2 model as described.
You can use Define to create the product and then not declare it as a Within variable - that way it will be latent-variable decomposed and the latent between part can be used on Level 2 as a predictor. The question is - from a substantive point of view - should the interaction be latent variable decomposed (as what I described) or should each variable be latent variable decomposed and then on Level 2 be made into an interaction (e.g. by putting a factor behind each on Level 2 and using XWITH).