3-way interaction
Message/Author
 Alyson Zalta posted on Thursday, February 01, 2007 - 7:22 am
Hello,
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?

Sailor
 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):

XW | X XWITH W;
XWZ | XW XWITH Z;

Y ON X W Z XW XWZ;

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.

 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)?

Regards

Tom Norton
 Bengt O. Muthen posted on Tuesday, August 25, 2015 - 6:33 am
Yes, if you have 2-level data.
 Buta Urge posted on Monday, June 20, 2016 - 3:23 am
Dear Profs. Muthen,
I am happy if you refer me to any information which explain:
How Mplus (LMS approach) calculate 3-way continuous latent variable interaction? is it based on the Klein and Moosbrugger(2000) article? The assumption based on this article was for two-way interaction.

Thank you very much
 Tihomir Asparouhov posted on Monday, June 20, 2016 - 5:15 pm
We use the method described in Section 6.4

It is full information ML via numerical integration.
 Buta Urge posted on Tuesday, June 21, 2016 - 8:09 am
Thank you Tihomir
 Birhanu Worku posted on Saturday, August 06, 2016 - 11:48 am
Hi
I derived R -square for three way latent interaction. In monte carlo simulation,can i use the derived R-square formula to fix the value of the residual variance for the dependent latent variable?or
I use R-square= 1-residual variance of the dependent latent variable ?

Thanks
 Bengt O. Muthen posted on Saturday, August 06, 2016 - 3:20 pm
R-square = 1 - residual variance is only true for the standardized residual variance.

Latent variable interactions
 Birhanu Worku posted on Sunday, August 07, 2016 - 1:18 am
Thank you Prof Bengt, I think i did wrong in simulation.
I set value for residual variance for dependent latent variable=0.4
I think the derived formula for R-square must not give me R-square=0.6 right?
After inserting population values here is what i got from the formula with residual var=0.4:
Total variance for dependent=1.68
R-square =0.76

let me hear from you whether i made mistake

Thanks
 Bengt O. Muthen posted on Monday, August 08, 2016 - 3:34 pm
R-square = 0.76.
 Birhanu Worku posted on Monday, August 08, 2016 - 11:20 pm
Thank you prof
 Jordan posted on Saturday, December 16, 2017 - 9:43 am
I am attempting to analyze a three-way interaction using the XWITH command.

It appears that the order in which I list the interactions in the syntax greatly influences the results.

For the three-way interaction, I first list the three two-way interactions, and then the three-way interaction:

2wayA (defined by x XWITH y)
2wayB (defined by x XWITH z)
2wayC (defined by y XWITH z)
3way (defined in this case by 2wayA XWITH z).

But if I place the 3way interaction after 2wayA, I get a completely different result, even though everything is defined the same way.

Which is the correct analysis?
 Bengt O. Muthen posted on Saturday, December 16, 2017 - 2:39 pm