I am using XWITH to test for moderating effects which works fine. Now I am writing on the technical part of my thesis and am not sure if I completely know what MPlus is doing when doing analysis with XWITH. I read that modelling moderating effects in covariance based software is a problem as they are working with the premise that the error terms of the indicator variables are uncorrelated. Thus I have three questions:
1. Does MPlus work with moderation as described by Baron & Kenny or does it apply a different approach. If so which and where can I read about it? 2. How does MPlus work “around” the premis of uncorrelated error terms of indicator variables – is there a paper I can read about it?
1. The approach used by Mplus is described in the Klein and Moosbrugger article cited in the user's guide. The elgorithm is slightly different. See also:
Moosbrugger, H., Schermelleh-Engel, K., Kelava; A. & Klein, A. G (2009). Testing multiple nonlinear effects in structural equation modeling: A comparison of alternative estimation approaches. Invited Chapter in T. Teo & M. S. Khine (Eds.), Structural Equation Modelling in Educational Research: Concepts and Applications. Rotterdam, NL: Sense Publishers.
2. This is not as issue with the approach Mplus uses.
For a comparison of the ML versus the product approach, see an article by Marsh et a. in Psych Methods several years ago.