Structural after measurement (SAM) approaches for accommodating latent quadratic and interaction effects.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Traditional methods for latent quadratic and interaction effects in structural equation models (SEMs), such as Unconstrained Product Indicator (UPI) and Latent Moderated Structural Equations (LMS), are effective for simpler models.
• Model complexity increases with numerous nonlinear terms, diminishing the feasibility of one-step estimation methods like UPI and LMS.

Purpose of the Study:

• To propose and evaluate Structural After Measurement (SAM) approaches as an alternative for estimating nonlinear effects in complex SEMs.
• To introduce a novel local SAM method and compare its performance with existing SAM techniques and traditional one-step methods.

Main Methods:

• The study advocates for a two-stage estimation process: first, estimating measurement parameters, and second, estimating structural parameters (SAM approach).
• Three existing SAM approaches are discussed, alongside a newly proposed local SAM method.
• A simulation study is conducted to assess the utility and performance of the SAM approaches.

Main Results:

• SAM approaches provide a practical and viable strategy for handling latent quadratic and interaction effects in SEMs.
• The simulation study demonstrates the effectiveness of SAM methods, particularly in models with increased complexity compared to one-step methods.

Conclusions:

• Structural After Measurement (SAM) approaches offer a robust alternative to established one-step methods for complex SEMs with multiple nonlinear effects.
• The proposed local SAM method and other SAM strategies are recommended for researchers dealing with intricate structural models.