A Simulation Study Comparing Recent Approaches for the Estimation of Nonlinear Effects in SEM Under the Condition of Nonnormality

Abstract

In the past decade new approaches for the estimation of latent nonlinear interaction and quadratic effects in structural equation modeling have been proposed (Kelava & Brandt, 2009; Klein & Moosbrugger, 2000; Klein & Muthén, 2007; Marsh, Wen, & Hau, 2004; Mooijaart & Bentler, 2010; Wall & Amemiya, 2003). Most approaches have been developed for the analysis of normally distributed latent predictor variables. In this article, we investigate the performance of five recent approaches under the condition of nonnormally distributed data: the extended unconstrained approach (Kelava & Brandt, 2009), LMS (Klein & Moosbrugger, 2000), QML (Klein & Muthén, 2007), the 2SMM approach (Wall & Amemiya, 2003), and the method of moments approach by Mooijaart and Bentler (2010). Advantages and limitations of the approaches are discussed.

Keywords:

• estimators
• interaction
• nonlinear structural equation models
• nonnormality
• quadratic

Notes

1. ¹Wall and Amemiya (2003) used a set of equations including higher order moments. These higher order moments can either be estimated or assumed to be zero if normality of the residuals is assumed.

2. ²For the interaction model actually the term unconstrained approach (Marsh et al., 2004, 2006) would be more adequate, but for simplicity we refer to the approach as ExUC approach throughout the rest of the article, which is the more general approach.