Have you looked into multigroup analysis?  Is that what you're after?

If so, you can do multigroup analysis in lavaan fairly easily or, if you're 
using the sem package, drop me a line.  I have some scripts that will do 
multigroup analysis for an equal sample size.

See 
http://faculty.chass.ncsu.edu/garson/PA765/structur.htm#multiplegroupanalysis
and
http://www.structuralequations.com/3.html

for some examples.

On May 25, 2010, at 8:38 AM, Anthony Dick wrote:

> Hello all,
> 
> This is a general stats question--I realize it is an R help list, so tell me 
> to go away if it is inappropriate.
> 
> I have a 2 X 2 design, and I have specified four identical path models (one 
> for each level of each factor). I want to test for an interaction at each 
> path--essentially (A1 - A2) - (B1 - B2) != 0. I was thinking of computing a 
> contrast for each path of interest, such that I compute the difference of the 
> difference in the (non-standardized) path weights (as above), and then divide 
> this by the pooled standard errors of the estimates (average of the standard 
> errors).
> 
> Does this seem statistically sound, or am I way off base? I typically compare 
> path weights across two levels (e.g., age differences in a path weight for 
> the same theoretical model) using the stacked model approach, but am not sure 
> how to apply this to the interaction.
> 
> Anthony
> 
> -- 
> Anthony Steven Dick, Ph.D.
> Post-Doctoral Fellow
> Human Neuroscience Laboratory
> Department of Neurology
> The University of Chicago
> 5841 S. Maryland Ave. MC-2030
> Chicago, IL 60637
> Phone: (773)-834-7770
> Email: ad...@uchicago.edu
> Web: http://home.uchicago.edu/~adick/
> 
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