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Mplus Discussion > Multilevel Data/Complex Sample >
 Anonymous posted on Thursday, November 03, 2005 - 1:40 pm
I'm hoping for an opinion about constraints in multilevel sem. I am developing a model were one latent variable varies across levels 1 and 2. Would it be advisable to constrain the factor loadings to be the same across both levels?

Keep in mind that I mean a complete sem not just cfa. Thank you.
 BMuthen posted on Thursday, November 03, 2005 - 5:38 pm
No, it would be inadvisable to constrain the factor loadings or other parameters across levels. Experience indicates that the same model will not fit at both levels.
 Ebrahim Hamedi posted on Sunday, September 02, 2012 - 5:05 pm
I am testing a multilevel model. I added factor loading equality constraints to the model, but failed to find any instructions about adding intercept constraints. Any help would be much appreciated.

this is the model with factor loading constraints:



fearhap by q1 q6 q2 q5 q3;

fearhap by q6(1);
fearhap by q2(2);
fearhap by q5(3);
fearhap by q3(4);


fearhap2 by q1;
fearhap2 by q6(1);
fearhap2 by q2(2);
fearhap2 by q5(3);
fearhap2 by q3(4);

Now, how can I add intercept constraints?

many thanks,
 Linda K. Muthen posted on Sunday, September 02, 2012 - 5:42 pm
Intercepts appear only in the between part of the model. There are no intercepts in the within part of the model.
 Ebrahim Hamedi posted on Sunday, September 02, 2012 - 6:17 pm
Thanks for your reply. Can you please let me know how to add this constraint. I am not sure about the syntax that I should use. Should it be something like:



[q1 q6 q2 q5 q3] (5);

in the between part? (I am doing this to examine scalar invariance of a 5-item scale).

many thanks,
 Linda K. Muthen posted on Sunday, September 02, 2012 - 7:46 pm
There are intercepts only on between in multilevel modeling. There is nothing to hold them equal to on within.
 Ebrahim Hamedi posted on Sunday, September 02, 2012 - 8:33 pm
Thanks. So as I though I cannot test scalar invariance in a two-level analysis.

what made me doubt my idea was this article wherein scalar invariance across two levels is tested:

on pages 10-11, authors write:

We conducted two separate lines of MCFA (multilevel confirmatory factor analysis analyses)..... For the two-item scale of LS, a good fit for the scalar invariance (RMSEA = 0.01; χ 2 = 14.42, df = 7) and an acceptable fit for the factor mean
invariance (RMSEA = 0.062; χ 2 = 1440.54, df = 19) models was established.

Pasted just for your info. Maybe my reading of the article is not accurate. Anyways, thank you very much for your answer. really helpful.

 Bengt O. Muthen posted on Tuesday, September 04, 2012 - 2:56 pm
I read their article and those pages don't make sense to me. Comparing countries with respect to indicator intercepts and factor means can only be done in conventional SEM by a multiple-group analysis, not a multi-level analysis. I will contact the authors to see what they did.
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