Multicollinearity and missing constraints: A comparison of three approaches for the analysis of latent nonlinear effects.

Multicollinearity complicates the simultaneous estimation of interaction and quadratic effects in structural equation modeling (SEM). So far, approaches developed within the Kenny-Judd (1984) tradition have failed to specify additional and necessary constraints on the measurement error covariances of the nonlinear indicators. Given that the constraints comprise, in part, latent linear predictor correlations, multicollinearity poses a problem for such approaches. Klein and Moosbrugger’s (2000) latent moderated structural equations approach (LMS) approach does not utilize nonlinear indicators and should therefore not be affected by this problem. In the context of a simulation study, we varied predictor correlation and the number of nonlinear effects in order to compare the performance of three approaches developed for the estimation of simultaneous nonlinear effects: Ping’s (1996) two-step approach, a correctly extended Joreskog-Yang (1996) approach, and LMS. Results show that in contrast to the Joreskog-Ya...