I am currently trying to create a latent interaction regression model in OpenMx where I have four latent variables (C, H, T, S) that predicts a fifth latent variable (A). In addition, interaction effects between the main latent predictor C, and H, T, and S should be included.
I am trying to figure out how to include interaction effects in SEM. Can I simply multiply the latent indicator variables? Marsh et al. (2012) decribes this as a problematic, and rather recommends a standardized solution first described by Wen, Marsh and Hau (2010). I am unsure how to implement such a model in OpenMx, however.
I'd be grateful for any input on what the best solution for including latent interactions would be, and how to implement them in an OpenMx model.
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We have some experimental code, but nothing I can recommend at this time.
Multiplying latent variables is tricky because you don't know their value. One way out is to 'pretend' that you know the value, which can be done in the context of quadrature. Bayesian methods are good at this sort of thing. I'd be interested to see a comparison.
https://openmx.ssri.psu.edu/thread/466