Structural Equation Modeling: Interaction between Latent Variables (Moderation)

[Mitja Kleczka]

Dear Statalist Community,

I am currently working on an article in the field of intercultural management. I have a number of control variables as well as four variables of interest, we can call them A, B, C and D. All four of them are not directly observed, but rather compose a combination of items taken from a questionnaire (they are latent variables). Because of this, it was decided to conduct the analysis using SEM in Stata.

The relationship to be modelled is as follows (for the sake of simplicity, I leave the controls out in this explanation):

1) A affects D
2) B affects D
3) C affects D
4) D is affected by the interaction between B and C (moderation). A higher/lower level of C changes the magnitude of the effect of B on D.

The problem here is number 4). I know how to conduct SEM using either the builder or the sem command, but I have not found a way of including an interaction between two latent variables in SEM regression using Stata. Is there any way of doing that?

If the variables were observed, the answer would be to simply construct an interaction term (as shown by Preacher, Rucker and Hayes: http://www.ats.ucla.edu/stat/stata/faq/modmed.htm), but unfortunately this is not the case. Leaving the moderation effect out of the regression or using a different procedure than SEM it out of question as well.

I have been reading a lot of literature on that topic but could not find any answer yet. Any help would hence be greatly appreciated.
Best,
Mitja Kleczka

[Jeff Pitblado (StataCorp)]

Wish I has a more constructive response here, but Stata's sem command does not allow interactions between latent variables.

[Mitja Kleczka]

Dear Jeff,

Thank you so much for the swift reply.
Although it is not exactly the answer I had hoped for, at least I know now that I can save the time of figuring out how to do it with Stata.

Best regards,
Mitja

[Guest]

Hi Jeff,

Try this: c.B#c.C

[Guest]

See if you can apply gsem instead. It does take interactions

[Christophe Haon]

Dear all,
Although gsem takes interactions, it doesn't work with summary statistics (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

[Bruce Weaver]

Apologies for resurrecting a 5-year old thread, but it came up in a search, and it seemed as good a place as any to add the following.

First, regarding the original question, this article suggests that one could implement the product indicator method via -sem-. Here is the complete citation:

Schoemann, A. M., & Jorgensen, T. D. (2021). Testing and interpreting latent variable interactions using the semTools package. Psych, 3(3), 322-335.

Second, posts #5 and #6 suggest that -gsem- has some way to estimate interactions between latent variables. Is that true? If so, can anyone direct me to some examples?

Cheers,
Bruce