SEM interaction analyses and centerin... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Anonymous posted on Tuesday, July 19, 2005 - 1:55 pm
I want to investigate potential interaction effects between two latent contious variables on a dependent latent continous variable in a SEM model (similar to textbook example 5.13). Do you recommend to center (= substract the mean) of the observed indicators of the latent constructs before running the model, as often announced in textbook for conventional moderator analyses?
 bmuthen posted on Tuesday, July 19, 2005 - 2:18 pm
No, that is not necessary when using the Mplus approach (I think Klein advocated this but that was using a slightly different parameterization) - the intercept parameters in the model will capture the indicator means properly even without centering them.
 Elmar posted on Friday, September 02, 2005 - 2:54 am
may I ask a follow up:

The setting:
I have hierachically structered data (280 persons in 90 organizations). I now need to model interaction effects between
two observed continous indicators, that is one individual- and one organisational variable.
My question:
Does the Mplus-approach in the Complex-procedure imply that I do not need to center the variables?
Many thanks,
 bmuthen posted on Friday, September 02, 2005 - 8:59 am
You can handle this in two ways, using Type=Twolevel or Type = Complex. With two-level analysis the interaction is captured by having a level 1 random slope for your individual-variable relationship which on level 2 is regressed on the between-level (organizational) variable. With complex analysis you simply create a product variable from the individual and organizational variables using Define; no centering needed, although that can help the interpretation.
 sammy posted on Tuesday, February 12, 2008 - 1:16 am

is it also possible to analyze the effect of interaction terms in a path analysis when the data-file consists of a correlation matrix?
Is it correct to calculate the correlation between the interaction terms and the rest of the variables and insert this new correlation matrix?

Thank you for your help!
 Linda K. Muthen posted on Tuesday, February 12, 2008 - 9:37 am
In Mplus you need raw data for models with interactions.
 Elizabeth Penela posted on Thursday, June 07, 2012 - 5:57 am

I am creating an interaction term between a latent factor and an observed variable using the xwith command. From reading posts above, it seems that it is not necessary to center the indicators of the latent variable.

However - is it necessary to center the observed variable?

Thanks for your help.

 Linda K. Muthen posted on Thursday, June 07, 2012 - 7:28 am
Right. Center only the observed variable.
 Elizabeth Penela posted on Thursday, June 07, 2012 - 8:17 am
OK- great. Thanks!

 Stefan Schneider posted on Wednesday, October 16, 2013 - 1:27 pm
I am estimating a model with two latent variables and their interaction ("xwith") predicting an observed variable. Both latent variables are standardized with a mean of zero and variance of one. Based on the short course topic 3 handouts (page 168), I am assuming that the estimated intercept of the observed outcome variable should represent its mean in this case (given that the mean of the latent variables is zero). Is this correct? I'm unsure because I noticed that adding the latent variable interaction to the model slightly changes the estimated intercept of the outcome variable, whereas the intercept is virtually identical to the observed mean of the outcome in a model without the interaction.
Thanks in advance for your input!
 Bengt O. Muthen posted on Thursday, October 17, 2013 - 6:17 am
The mean of an interaction is not zero even though each of the two variables has mean zero. This is described in the FAQ "Latent variable interactions." The mean is a function of the covariance of the two variables.
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