Specification of level 2 latent variabels in Multi-level SEM

[Teresa O.]

I am conducting a two-level SEM and found the tutorial here initially very helpful: http://lavaan.ugent.be/tutorial/multilevel.html. Upon second glance, however, I am wondering if there is an error in the specification for the second level latent variable. It seems that both the within and between factor uses the same variables (x1, x2, x3). I am wondering if the second level variables should instead be means for the three variables (x1, x2, x3) for each of the 200 clusters?

I only mention this because a colleague had corrected a model that I had previously parameterized incorrectly, and afterwards realized that not only the model fit, but the clarity of its interpretation were much improved.

At the very least, I wonder if this could be a possible source of confusion. I think the functionality of analyzing a 2-level SEM is wonderful and hope that this tutorial is as helpful to others, as well.

[Terrence Jorgensen]

I am wondering if the second level variables should instead be means for the three variables (x1, x2, x3) for each of the 200 clusters?

By virtue of the Level 2 construct being specified in the "Level: 2" block of the syntax, that will happen automatically.  Actually, it will be measured by the latent cluster-level component of those variables (cluster means are biased estimates of those, which is why MSEM is preferred over ad hoc methods of disaggregating components in MLM).

http://dx.doi.org/10.1037/a0024376

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen