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.