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 Xu, Man posted on Monday, January 18, 2010 - 8:44 pm
Hi, I am interested in how an additonal predictor variable(X) could partial out the effect that a between level variable (W) has on Y. So I included X as predictor on the within level without specifying this variable to be level 1 or level 2. The between level variable W's effect on Y was not changed.
While I tried the same (I think it was the same) model in MLwin, after adding X, the effect W had on Y was substantially reduced. So I think I must have not set up the same model in Mplus.
I was wondering how I set up the syntax in Mplus to get comparable results as in MLwin please? Thanks!
 Linda K. Muthen posted on Tuesday, January 19, 2010 - 2:21 pm
If you have not put x on the WITHIN list, this may be the problem. If not, please send the Mplus and MLwin output and your license number to support@statmodel.com. See also Examples 9.1 and 9.2 in the user's guide.
 Xu, Man posted on Wednesday, January 20, 2010 - 1:43 pm
Thank you Linda. That's so very helpful. I indeed failed to include the x in the WITHIN list. Now my problem has been solved. There is now only 0.002 difference in the estimates between Mplus (with multiple imputation) and MLwin (with listwise deletion). so I think it is close enough to be seen as equal.
Was the previous problem due to the latent variance decomposition of x such that, without declaring x to be a within variable, only the within variances of x was used to predict the variance in the outcome?
but why x can explain y on the between level as a within predictor, but not so when it was not declared to be a within predictor?
 Linda K. Muthen posted on Wednesday, January 20, 2010 - 3:48 pm
Yes, the previous difference was due to the latent variable decomposition of x.

This phenomenon is discussed in the multilevel literature. See for example Raudenbush and Bryk.
 Xu, Man posted on Wednesday, January 20, 2010 - 5:42 pm
Thank you Linda. I remember reading Raudenbush and Bryk (it's not at hand at the moment). In Mplus, I used the model constraint method to get the contextual effect of a variable Q using latent variable decomposition. After adding the control variable x that we jsut discussed about, the contextual effect of Q changed much. Is this still a valid estimate of contextual effect of Q? I remember reading from somewhere that the constraint method was only good for when there is no other control variable present.
 Xu, Man posted on Wednesday, January 20, 2010 - 6:45 pm
to clarify myself further, what confuses me most now is that, when i use the traditional contextual approach (group average of the within variable as a between variable) to test Q's effect on the outcome, after adding x (without listing to be WITHIN) as a control in the within level model, the contextual effect does not change. But when I use the latent decomposition of Q with CONSTRAINT to obtain the contextual effect, with the same settings for Q, the contextual effect of Q mostly disappeared.
I understood that the change in the CONSTRAINT estimate was due to collinearlity between Q and the control x. But when x was not listed to be within, the contextual effects from the both methods are really very different and not comparable at all. Was the estimate of contextual effect wrong in the CONSTRAINT method under such settings of x?
 Bengt O. Muthen posted on Wednesday, January 20, 2010 - 8:36 pm
This is a large topic - please see

Lüdtke, O., Marsh, H.W., Robitzsch, A., Trautwein, U., Asparouhov, T., & Muthén, B. (2008). The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies. Psychological Methods, 13, 203-229.

which is on our web site.
 Xu, Man posted on Thursday, January 21, 2010 - 12:09 am
thanks for the reference! Then do you think in general it is good to declare a predictor variable to be WITHIN when its own contextual effect is not of particular interests?
 Bengt O. Muthen posted on Thursday, January 21, 2010 - 4:06 pm
I wouldn't want to comment on that from a substantive perspective since I don't know the subject-matter. Statistically speaking, I would include a contextual effect (using either the latent decomposition or the manifest cluster mean) whenever it is significant.
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