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 Dana Weiser posted on Monday, February 06, 2012 - 7:57 pm
Hello,

I am trying to model interactions between an observed continuous variable (age) and 3 latent variables. I have read your Modeling Interactions Webnotes from March 2003. In the article, it states that such an interaction is not supported by conventional SEM and you refer to additional readings focusing on the Joreskog-Yang approach, 2SLS, and the full-information maximum-likelihood approach. My question is, does MPlus allow me to utilize such models, and if so, how? Thank you so much!
 Linda K. Muthen posted on Monday, February 06, 2012 - 8:00 pm
Mplus takes the full-information maximum likelihood approach using the XWITH option.
 Dana Weiser posted on Monday, February 06, 2012 - 9:19 pm
Thank you! So would I just model the interaction normally?
For a simplified version, say Z is the observed continuous variable:

MODEL: X BY x1-x3;
Y BY y1-y3;
INT | X XWITH Z;
X WITH Z;
Y ON X Z INT;
 Linda K. Muthen posted on Monday, February 06, 2012 - 10:01 pm
Yes. I would not include the interaction between the covariates. The model is estimated conditioned on them and when you mention their means, variances, or covariances they are treated as dependent variables and distributional assumptions are made about them. Model estimation does not fix them at zero.
 Dana Weiser posted on Monday, February 06, 2012 - 10:27 pm
Great. Thank you!
 Student 09 posted on Friday, February 10, 2012 - 7:20 pm
Hello,

when testing interaction effects, variables are often centred around their mean.
When the variables are factors (= latent variables, e.g. f1 by x1 x2 x3), is centering still necessary?
 Dana  posted on Friday, February 10, 2012 - 10:38 pm
When testing an interaction between two latent variables you do not need to center.
 Bengt O. Muthen posted on Friday, February 10, 2012 - 10:45 pm
Typically, latent variables have mean zero so centering is already implicit. Although not necessarily in growth and multi-group models.
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