Covariances with latent interactions PreviousNext
Mplus Discussion > Categorical Data Modeling >
 Carol M. Woods posted on Thursday, July 01, 2010 - 11:30 am

I'm fitting a MIMIC model using categorical indicators and MLR. The model includes an interaction between a continuous random latent variable (theta) and an observed causal indicator (z) defined using XWITH and |.

It seems that by default the covariances between the interaction and theta and the interaction and z are 0. Is it possible to estimate these covariances?
 Linda K. Muthen posted on Friday, July 02, 2010 - 9:44 am
The only parameter that is associated with a latent variable interaction is the slope.
 Carol M. Woods posted on Friday, July 02, 2010 - 6:37 pm
Thanks for the reply.

I'm having difficulty finding documentation describing the methods implemented for the latent variable interactions. Is there a technical appendix?

We found something that said procedures were in line with Klein & Moosbrugger (2000). But Marsh et al. (2004) says that LMS method was superseded by the QML method in Klein & Muthen (2002) -- is that in Mplus? Either way, is it possible to get that unpublished paper?
 Linda K. Muthen posted on Saturday, July 03, 2010 - 9:49 am
Mplus does not use QML. Mplus uses maximum likelihood which is the same as LMS but using a different algorithm.

The paper has been published:

Klein and Muthen (2007). Quasi-maximum likelihood estimation of structural equation models with multiple interaction and quadratic effects. Multivariate Behavioral Research, 42, 647-673.
 Carol M. Woods posted on Tuesday, October 12, 2010 - 7:37 am

Another question about this same project. I'm trying to keep track of the assumptions made by LMS. Are we assuming the 2 variables involved in the interaction are continuous, latent, and bivariate normal? I am interacting one continuous latent with one observed binary.

Is there also an assumption that the observed indicators of those latent variables are continuous and normal? So it's not good to be using LMS with categorical observed data (even though I'm using "categorical" and MLR)?

Is there something about the "different algorithm" for LMS that would make it OK to do what I'm doing? Seems like I'm violating 2 by using LMS with this model.

 Linda K. Muthen posted on Wednesday, October 13, 2010 - 12:19 pm
In an interaction model, it is assumed that the latent variables are normally distributed. It is not assumed that the factor indicators are normally distributed.
 Carol M. Woods posted on Wednesday, October 13, 2010 - 2:41 pm

Is there something new in version 6 for this -- I'm seeing "XWITH Multiple group" in the manual. What does that do?
 Linda K. Muthen posted on Wednesday, October 13, 2010 - 4:56 pm
I don't know of anything new. And I don't know where in the user's guide you see this. You will need to give me a page number.
 Carol M. Woods posted on Thursday, October 14, 2010 - 7:08 am
On page 612, the table that says how to obtain interactions between different types of variables. For the case of an observed categorical with a continuous latent, it says "XWITH multiple group".
 Linda K. Muthen posted on Thursday, October 14, 2010 - 7:30 am
This means that you can use XWITH or multiple group analysis to test the interaction between an observed categorical variable and a continuous latent variable. With multiple group analysis, you use the observed categorical variable as a grouping variable.
 Luke W. Hyde posted on Thursday, February 10, 2011 - 7:52 am
Dear Drs. Muthen,

I'm running an SEM with two interactions using the XWITH command. One of the interactions involves a binary observed variable and a continuous latent variable. The binary variable itself is essentially exogenous - it only predicts other variables and is not predicted by variables in the model. Should this variable be signified to the model as categorical? Given its involvement in an interaction is the variable technically an independent or dependent variable?

I have run the model with the variable specified as categorical or and also without this specification. When the variable is specified as categorical, the model runs and terminates normally. When it is not specified as categorical, the model cannot terminate normally and has various not-positive definite errors (and even when changing other terms to fix the error, another error comes up). I was initially assuming the problem running the model was multicolinearity with 2 interaction terms.Is that possible?

So my main questions are:
1. Should I specify this categorical variable as categorical in the model?
2. If I shouldn't, are there anyways to decrease multicolinearity with 2 interactions (involving 2 continous, 1 categorical variable) within the same model?

Thank you very much for your time.
 Linda K. Muthen posted on Thursday, February 10, 2011 - 11:07 am
This variable is exogenous and should not be put on the CATEGORICAL list. If you have problems when it is not on the list, please send the output and your license number to
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