Moderators with Latent Variables

[Ryne Sherman]

Hi All,

Does lavaan support this sort of thing? Last I knew (which was some years ago now), there was no consensus on how to create proper interaction terms with latent variables. Is this still the case? The page gives guidance on how to examine interactions with latent variables in MPlus: http://www.offbeat.group.shef.ac.uk/FIO/model3latent.htm

The key section of the MPlus code seems to be this: 

! Create latent interactions 
   XW | X XWITH W; 
   XZ | X XWITH Z; 
   WZ | W XWITH Z; 
   XWZ | XW XWITH Z;

Any idea how MPlus is creating latent interactions? Can this be doen in lavaan? In R? 

For context, I'm reviewing a dissertation where the student used this sort of analyses / syntax. The results look funny and I'm trying to pinpoint why. I'm hoping that replicating the student's analyses in R will help, but I'm not sure if that is possible. 

Cheers,

-Ryne

[Ryne Sherman]

For what it is worth, I'm aware of the "products of indicators" method (generally, I've never actually done it myself). In this particular case one latent variable has 7 indicators and the other has 8, which seems like an awful lot of products to make into indicators. But, perhaps that what MPlus is doing???

[Alex Schoemann]

Hi Ryne,

Mplus is using non-linear SEM to estimate interaction terms among latent variables, for a nice review see Moosbrugger et al (2009). This is different from a product of indicators approach, but both approaches work pretty well (one may be better than the other depending on the situation). I believe the non-linear SEM approach is available in the nlsem package in R (https://cran.r-project.org/web/packages/nlsem/index.html). 

Alex

Moosbrugger, H., Schermelleh-Engel, K., Kelava; A. & Klein, A. G (2009). Testing multiple nonlinear effects in structural equation modeling: A comparison of alternative estimation approaches. Invited Chapter in T. Teo & M. S. Khine (Eds.), Structural Equation Modelling in Educational Research: Concepts and Applications. Rotterdam, NL: Sense Publishers. Available at: http://statmodel.com/download/Moosbrugger.pdf 

[Ryne Sherman]

Thanks Alex! Much appreciated! 

-Ryne