Hi,
Are there any simple procedures in OpenMx that allow us to estimate interactive effects of latent variables? It is possible, of course, to use the Kenny-Judd method to specify the latent product variables "by hand", and to estimate the product indicators and the variances of the latent product variables. However, product variables are generally not normally distributed even if their component variables are normally distributed. I recently read that Klein and colleagues suggested approaches that take into account the degree of non-normality implied by the latent product terms. Klein and Moosbrugger (2000) suggested the "latent moderated structural equations method", which uses a form of the expectation-maximization (EM) algorithm. Klein and Muthén (2006) suggested the "quasi-maximum likelihood estimation method", which uses a simpler algorithm but closely approximates results of the former method. Have any of these approaches been incorporated in OpenMx?
See
Neale, M.C. (1998) Modeling interaction and nonlinear effects with Mx: A general approach. In: G. Marcoulides & R. Schumacker Interaction and Non-linear Effects in Structural Equation Modeling pp. 43-61. New York: Lawrence Erlbaum Associates http://www.vipbg.vcu.edu/vipbg/Articles/Chap3-ModelingInteraction-43.pdf
for a generalization of Kenny & Judd as an approach for interactive effects of latent variables. I would also consider marginal maximum likelihood methods, such as those recently elaborated by Dylan Molenaar:
http://www.dylanmolenaar.nl/index.php?option=com_content&view=category&layout=blog&id=10&Itemid=9
as these could be used via mixture distribution analysis. OpenMx is functionally compatible with classic Mx, so Mx scripts can be implemented in OpenMx (though the reverse is not always the case).
The link to the Molenaar paper is no longer working. Is this the paper you were referring to?
It's been a decade... that may be the one I had in mind. This one also looks useful href="http://www.dylanmolenaar.nl/Murray%20et%20al.%20BGA.pdf" from Dylan's homepage
Here is an archival copy of the scripts that Mike linked to 10 years ago. https://web.archive.org/web/20141002135916/http://www.dylanmolenaar.nl/index.php?option=com_content&view=category&layout=blog&id=10&Itemid=9
Here is an archival copy of the page Mike linked to 10 years ago https://web.archive.org/web/20141002135916/http://www.dylanmolenaar.nl/index.php?option=com_content&view=category&layout=blog&id=10&Itemid=9
Turns out is was the same article I linked. =)
Hi
We have new algorithms for estimating the effects of interactions among latent variables, due to fundamental work by Dr. Steve Boker. They come with an upgrade to conventional path diagrams, for ease of communication. The new features will be released in beta in the near future (my guess is within a month). Simulations check out nicely, and Dr. Boker is preparing an article describing the new software.
I am curious a to which approaches to latent interaction will be available. Are they established product indicator and/or distribution analytic approaches, or new approaches entirely?
This is a new approach. It is available (but not documented) in the current release. If you want to try it out, drop me a line to boker at virginia dot edu.