Hello,

I have seen that the standard way to model a GxE-moderation with OpenMx is using the "definiton variable"-approach with the moderator as a manifest definition variable. When my moderator is a latent variable it seems to me that the definition variable approach is only viable if I create the latent variable before eg. with a CFA and use it then as a "normal" variable in my data set. But I think the best way would be to integrate the measurement model into the GxE-model to assess the fit of both together. My questions is: Is it possible (a) to integrate a measurement model for the moderator in a GxE-model with OpenMx and (b) model a lantent interaction between the latent variance components and the latent moderator? I have read in the forum that it is possible to model a latent interaction with OpenMx, so actually it should not be a problem to model a latent interaction in a GxE-model or am I missing something?

Yes, most things are possible with OpenMx. Not all are convenient. In part this is because we had hoped for more build-out from the community in terms of higher-level functions to perform specific activities. There have been some - umx, ezmx, ctsem, metasem for example, but more would be welcome.

You may want to to know how to do this... one way would be to integrate over the latent variable by specifying a mixture distribution with Gaussian quadrature weights over the latent E and latent G variables. This is not very convenient, even if mxEvaluateOnGrid() was used to handle some of the housekeeping. Another approach might be to adapt Baron & Kenny's approach of feeding the software products of the observed variables, which I took for a walk down matrix algebra lane in this article (https://vipbg.vcu.edu/vipbg/Articles/Chap3-ModelingInteraction-43.pdf) - it's perhaps the earliest one to talk about definition variables although the feature was originally developed in 1994). New methodology is on the way, though - OpenMx version 3.0 will include features for some new kinds of path analysis, including product of variables (latent or observed) in a relatively user-friendly and computationally efficient fashion.

Expectation-maximization might be useful for your purposes. Here's a thread containing some information and examples about

`mxComputeEM()`

.