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

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Assessing nonlinear relationships in structural equation modeling (SEM) is complex.
• The performance of different SEM approaches for nonlinear terms requires investigation.

Purpose of the Study:

• To compare the extended unconstrained approach (EXUC) and latent moderated structural equation modeling (LMS) for testing quadratic and interaction terms.
• To identify limitations of EXUC and LMS concerning measurement properties like indicator reliability and type.

Main Methods:

• A Monte Carlo simulation study was employed.
• The study evaluated EXUC and LMS under various conditions, including sample size, indicator reliability, and indicator types (parallel vs. congeneric).

Main Results:

• Latent moderated structural equation modeling (LMS) is recommended for testing multiple nonlinear effects when sample size is sufficient (n ≥ 500) and exogenous variables are normally distributed.
• LMS demonstrated superior performance with heterogeneous and low indicator reliabilities.
• The extended unconstrained approach (EXUC) is a suitable alternative for models with parallel indicators and high reliability.

Conclusions:

• Measurement model characteristics significantly impact the assessment of nonlinear relationships.
• LMS offers a robust method for complex nonlinear SEM, especially with challenging measurement properties.
• EXUC provides a viable option under specific, favorable measurement conditions.