Reexamining Nonlinear Structural Equation Modeling Procedures: The Effect of Parallel and Congeneric Measures

Abstract

The current study examines the performance of the extended unconstrained approach (EXUC) and the latent moderated structural equation modeling procedure (LMS) in situations where quadratic and interaction terms are tested simultaneously and investigates their limitations with regard to the employment of parallel and congeneric measures, relatively low indicator reliabilities, and relatively large numbers of indicators. By means of a Monte Carlo study, we found LMS to be the best option for testing multiple nonlinear effects given sufficient sample size (n ≥ 500) and normally distributed exogenous variables. Its advantages became more prominent when indicator reliabilities were heterogeneous and small. The EXUC was a viable option for estimating the model when indicators were parallel and exhibited large indicator reliabilities. An empirical example of the results is provided, and the relevance of measurement model characteristics to assess nonlinear relationships is discussed.

KEYWORDS:

• extended unconstrained approach
• interaction effects
• latent moderated structural equations
• nonlinear SEM
• quadratic effects

Notes

LMS is implemented in Mplus (Muthén & Muthén, 2011) and EXUC can be implemented in any software capable of handling SEM.

Even though several options for creating the products for the interaction effect are available (e.g., all possible pairs), in order to keep the reuse of indicators to a minimum when assessing multiple nonlinear effects, the matched-pairs strategy (Marsh et al., 2004) is advised when both measurement models have the same number of indicators.

All results are available from authors upon request.