Structural equation modeling with summary statistics and interaction between latent variables

[Christophe Haon]

Dear all,

I am wondering whether it is possible to estimate a structural equation model with an interaction between two latent variables when one has summary statistics data (SSD).
sem works with SSD but not with interactions
gem takes interactions but not SSD

Has anyone a suggestion about how (if possible) I could estimate a model —based on a correlation matrix— with an interaction term?

Thanks,
Christophe

[Joseph Coveney]

I wasn't aware that gsem could fit an SEM that has interactions of latent variables (other than, say, cross-classified random effects). As to your question, you could create a dataset with the correlation matrix and use that with gsem. See

help corr2data

[Christophe Haon]

Will definitely look into that, thank you Joseph!

[Mikko Rönkkö]

Not possible. Consider the following: You have correlations three correlations of X1, X2, and Y. To estimate a model with an interaction with interaction of X1 and X2, you would be estimating three exogenous correlations and three regression paths. You cannot estimate six things from three things.