Structural equation models of latent interactions: evaluation of alternative estimation strategies and indicator construction.
Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches--unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The authors' new unconstrained approach was easiest to apply. All 4 approaches were relatively unbiased for normally distributed indicators, but the constrained and QML approaches were more biased for nonnormal data; the size and direction of the bias varied with the distribution but not with the sample size. QML had more power, but this advantage was qualified by consistently higher Type I error rates. The authors also compared general strategies for defining product indicators to represent the latent interaction factor.
Marsh
Herbert W
HW
Self-Concept Enhancement and Learning Facilitation Research Centre, University of Western Sydney, Sydney, New South Wales, Australia. h.marsh@uws.edu.au
Wen
Zhonglin
Z
Hau
Kit-Tai
KT
D000704:Analysis of Variance; D006801:Humans; D016013:Likelihood Functions; D008432:Mathematical Computing; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D011589:Psychology, Experimental / Q000706:statistics & numerical data*; D012984:Software