Published on *OpenMx* (http://openmx.psyc.virginia.edu)

By *kpreacher*

Created *09/28/2009 - 19:30*

Mon, 09/28/2009 - 19:30 — kpreacher [1]

Just wanted to get some discussion going.

The best method I have seen for diagramming multilevel SEM appears in Mehta and Neale (2005). Their method is very compact, and maps completely onto the matrix expression for two-level models. Random slopes are represented as latent variables with definition variables as loadings. The method has the further benefit of being "collapsible" in that variables treated in a redundant manner can be collapsed into single variables without becoming inconsistent with the matrix expression.

This method works well for 2-level models with manifest predictors, but if we wish to diagram a random slope for a latent predictor, there's nothing concrete to "put" in the loadings, so the method is not as general as one would hope. Other traditions represent multilevel SEM with distinct "within" and "between" submodels, and mark random coefficients in the "within" model with darkened circles, corresponding to latent variables in the "between" model. This notation is compact, and complete to those who know how to interpret the diagrams, but the mapping between matrix expression and diagram is not as 1-to-1 as for simpler models.

Another problem area involves diagramming latent variable interactions. I take it we don't want to have arrows pointing at other arrows (although arrows pointing at random slopes is okay if they are represented as latent variables), but neither do we want products of latent variables in the diagrams (or do we?).

**Links:**

[1] http://openmx.psyc.virginia.edu/users/kpreacher

[2] http://openmx.psyc.virginia.edu/thread/85

[3] http://openmx.psyc.virginia.edu/thread/48-welcome-graphical-user-interface-forum

[4] http://openmx.psyc.virginia.edu/forums/openmx-developer-forums/graphical-user-interface