3-way interaction PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Alyson Zalta posted on Thursday, February 01, 2007 - 7:22 am
I am interested in examining an interaction between 3 latent continuous variables. Is this possible in MPlus using the xwith option? If so, what is the syntax?
Thank you.
 Linda K. Muthen posted on Thursday, February 01, 2007 - 7:25 am
I think you can do this usng XWITH two times. Create the interaction for two latent variables in the first XWITH and use that interaction in the second XWITH along with the third latent variable.
 Alyson Zalta posted on Friday, February 02, 2007 - 7:30 am
Thank you for your quick response. I am using the 3-way interaction term as an independent variable. Do I need to include all two-way interactions in the ON statement as I would in a regression? Thanks again for your help.
 Linda K. Muthen posted on Friday, February 02, 2007 - 2:17 pm
I would do the same as in regular regression.
 sailor cai posted on Monday, January 21, 2013 - 7:07 pm
Dear Professors Muthens,

A question about three-way latent interaction using LMS on Mplus 7.0: How to standardize the coefficient of a three-way latent interaction?

Say, I have: Y= aA+bB+cC+ d(A*B)+e(A*B*C), how do I standardize e?

My understanding is that to standardize the coefficient of the two-way interaction d, we can do this:

d(standardized)= (sqtr of Variance of A) * (sqrt of the variance of B)/sqrt of variance of Y.

So, to standardized e, can we do it this way:

e(standardized)= (sqtr of Variance of A) * (sqrt of the variance of B)*(sqrt of the variance of B)/(sqrt of variance of Y).
If not, how can I standardize e?

Many thanks in advance!

 Bengt O. Muthen posted on Monday, January 21, 2013 - 7:55 pm
You should take a look at the FAQ "Latent Variable Interactions".
 Tamsyn Gilbertson posted on Tuesday, August 11, 2015 - 11:43 pm
Dear Profs. Muthen,

I've obtained a significant 3-way latent variable interaction using the following LMS syntax (measurement model omitted):



1. Is this the correct syntax for a 3-way latent variable interaction?

2. If so, can you recommend a way of plotting simple slopes based on the model output for the relationship between X and Y at different levels of the two moderators (e.g., W and Z both 1SD above the mean)?

The MODEL CONSTRAINT/LOOP function works wonderfully for my 2-way interactions, but I'm struggling to adapt it to 3-way interactions as specified using the above syntax. Alternative simple slopes tools seem to require all possible 2-way interactions between X, W and Z to be specified within the same 3-way model (e.g., http://www.quantpsy.org/interact/mlr3.htm), leading me to question my syntax.

Your advice would be greatly appreciated!
 Bengt O. Muthen posted on Wednesday, August 12, 2015 - 4:42 pm
1. Yes.

2. You will get a fuller answer by posting this general modeling question on SEMNET.
 tom norton posted on Monday, August 24, 2015 - 8:58 pm
Profs. Muthén

Is it possible to test a 3-way interaction by creating an interaction term among two level 1 variables, regressing the DV on the interaction term (creating slope s1), and then regressing s1 on the third variable (a level 2 variable)?


Tom Norton
 Bengt O. Muthen posted on Tuesday, August 25, 2015 - 6:33 am
Yes, if you have 2-level data.
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