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 James Lemoine posted on Tuesday, January 07, 2014 - 7:00 pm
Happy new year,

I would like to estimate a L2 outcome from L1 variables, and am struggling to locate correct syntax to utilize a multivariate manifest covariate approach in Mplus. The paper by Croon et al (2008) provides syntax for both the MLC and the MMC, but I can't get either to work in Mplus (I am using MMC rather than MLC as my L2 variable is a group for which I have all members reporting).

The syntax as reported in the paper is:
VARIABLES: names are classid math distract a_distract;
cluster is schoolid;
within = distract;
between = a_distract;
centering = groupmean(distract);
ANALYSIS: type is twolevel;
MODEL:
%within%
math on distract;
%between%
math on a_distract;

However, after replacing the "centering" line with the new DEFINE: center command, this still isn't working as there is no within group variance on (in this example) math, a level 2 variable.

Could someone please help me figure out if there is something about the syntax that I am misunderstanding, or if there is a change from 2008 syntax that I have missed? Again, I'm starting out with a single L1 predictor, but I'd eventually like to use both L1 and L2 variables to predict a L2 outcome. Thanks for any help you can provide.
 Bengt O. Muthen posted on Tuesday, January 07, 2014 - 7:24 pm
If math is an L2 variable it should appear on the Between list and not be mentioned in the Within part of the model.
 James Lemoine posted on Tuesday, January 07, 2014 - 8:19 pm
Thank you very much for the quick reply. If I'm understanding you correctly, then I would no longer be predicting math (a L2 outcome) with the within part of the model - instead, I'd just be using the mean of the L1 variable, aggregated, to predict at L2, which is not statistically ideal. I was under the impression that the MMC and the MLC allowed you to use L1 variables to predict an L2 outcome. Would this all be accomplished in Mplus through the between model? How would this go beyond simple aggregation of the L1 variable, as it's discussed in your paper?

Thanks very much for any guidance you can provide.
 Bengt O. Muthen posted on Tuesday, January 07, 2014 - 8:42 pm
You can predict an L2 variable by the between part of a variable measured on subjects (L1). Mplus can do this using a latent variable decomposition - in your example this refers to the "distract" variable", so delete the 2 lines:

within = distract;
between = a_distract;

add the line:

between=math;

and say:

MODEL:
%within%
distract;
%between%
math on distract;
 James Lemoine posted on Tuesday, January 07, 2014 - 10:59 pm
Thank you, sir - that seems to be running well. If I may ask one more question, how would this model respond to multiple Level 1 predictors that might be highly correlated? My predictors are different classes of membership at Level 1, and each member is a different class. I have dummies for all but one of the different classes, but am concerned about multicollinearity if I put them all in together.
 Bengt O. Muthen posted on Thursday, January 09, 2014 - 2:35 pm
Not sure why these multiple dummies would be so highly correlated, but if they are you would be affected as in regular regression. If they are, perhaps you want to consider a factor behind them to be the more useful predictor - that avoids the collinearity.
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