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. 


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. 


Thank you for your quick response. I am using the 3way interaction term as an independent variable. Do I need to include all twoway interactions in the ON statement as I would in a regression? Thanks again for your help. 


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 threeway latent interaction using LMS on Mplus 7.0: How to standardize the coefficient of a threeway 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 twoway 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! Sailor 


You should take a look at the FAQ "Latent Variable Interactions". 


Dear Profs. Muthen, I've obtained a significant 3way 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 3way 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 2way interactions, but I'm struggling to adapt it to 3way interactions as specified using the above syntax. Alternative simple slopes tools seem to require all possible 2way interactions between X, W and Z to be specified within the same 3way model (e.g., http://www.quantpsy.org/interact/mlr3.htm), leading me to question my syntax. Your advice would be greatly appreciated! 


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 3way 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 


Yes, if you have 2level 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 3way continuous latent variable interaction? is it based on the Klein and Moosbrugger(2000) article? The assumption based on this article was for twoway interaction. Thank you very much 


We use the method described in Section 6.4 http://statmodel.com/download/ChapmanHall06V24.pdf It is full information ML via numerical integration. 

Buta Urge posted on Tuesday, June 21, 2016  8:09 am



Thank you Tihomir 


Hi I derived R square for three way latent interaction. In monte carlo simulation,can i use the derived Rsquare formula to fix the value of the residual variance for the dependent latent variable?or I use Rsquare= 1residual variance of the dependent latent variable ? Thanks 


Rsquare = 1  residual variance is only true for the standardized residual variance. See also Section 2 of our FAQ: Latent variable interactions 


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 Rsquare must not give me Rsquare=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 Rsquare =0.76 let me hear from you whether i made mistake Thanks 


Rsquare = 0.76. 


Thank you prof 

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