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 Xu, Man posted on Thursday, October 30, 2008 - 12:40 am
I am interested in the SEM only in the first level; however, if I need to take into account of the multilevel structure, is multilevel SEM the best way to do it, even if I am not really interested in level 2 results? (I assume that the SEM model on the second level should have the same model specification as the first level except for using group level indicators of the level 1 indicators for level 2 factors, constraining loadings to be the same as corresponding level 1 factors)
Thank you!
 Linda K. Muthen posted on Thursday, October 30, 2008 - 8:16 am
It is not likely that the between specification would be the same as the within specification. Usually there are fewer factors on between than within. You can explore the between-level factor structure using TYPE=TWOLEVEL EFA.
 Xu, Man posted on Wednesday, November 05, 2008 - 9:11 am
Thank you for your help. I guess I am trying to get a similar thing as in multilevel regression random intercept models. Could there be an analogue in multilevel SEM where the level 1 intercepts of each indicators are free for each cluster instead of having to specify something on the higher level?
 Linda K. Muthen posted on Thursday, November 06, 2008 - 8:40 am
You can specify your SEM model on level 1 and covariances among the random intercepts on level 2. See Example 9.6. The between part would be:

y1 WITH y2 y3 y4;
y2 WITH y3 y4;
y3 WITH y4;

These WITH statements are covariances among the random intercepts.
 Xu, Man posted on Tuesday, November 11, 2008 - 3:36 am
Is allowing covariance at level 2 a strategy for increasing fit?
Can I just leave the between bit empty?
 Linda K. Muthen posted on Wednesday, November 12, 2008 - 8:17 am
If you do not want to specify a particular model on the between level, it probably makes sense to have a saturated model.
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