There are several approaches for modeling latent interactions (constrained and unconstrained product indicator approach, LMS, QML, ...). Although there are several simulation papers which show that for non-normal latent variables estimates may be (extremely) biased, all approaches assume continuous indicators. For linear SEM it seems to me that the “correct treatment” of ordinal indicators (eg. WLSMV-estimation in Mplus) becomes more common. But what is about this topic in nonlinear SEM?
Dear L. Mónico,
thanks a lot. But actually methodological papers on latent interactions (e.g. Lin et al., 2010; Cham et al., 2012; Brandt et al., 2014) assume continuous indicators and use Satorra-Bentler- or similar corrections. Brandt et al. (2014) state that further research on latent interactions has to be extended to the use of ordinal or censored indicators. And here lies my interest, has the research already been extended?
Lin, G. C., Wen, Z., Marsh, H. W., & Lin, H. S. (2010). Structural equation models of latent interactions: Clarification of orthogonalizing and double-mean-centering strategies. Structural Equation Modeling, 17(3), 374-391.
Cham, H., West, S. G., Ma, Y., & Aiken, L. S. (2012). Estimating latent variable interactions with nonnormal observed data: A comparison of four approaches. Multivariate behavioral research, 47(6), 840-876.
Brandt, H., Kelava, A., & Klein, A. (2014). A simulation study comparing recent approaches for the estimation of nonlinear effects in SEM under the condition of nonnormality. Structural equation modeling: a multidisciplinary journal, 21(2), 181-195.
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