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Interaction among latent variables

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brauer's picture
Joined: 01/28/2012 - 11:34
Interaction among latent variables


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?

neale's picture
Joined: 07/31/2009 - 15:14
Matrix algebra helps


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

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:

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).

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