Structural equation modeling with factors and composites within the framework of the basic design.

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Partial Least Squares Structural Equation Modeling (PLS-SEM) is widely used but has theoretical and convergence limitations.
• Existing methods like PLS-PM, PLSc, and composite models lack robust theoretical foundations.
• Iterative algorithms in PLS-SEM do not guarantee convergence, impacting reliability.

Purpose of the Study:

• To introduce SVD-SEM, a novel, non-iterative method for structural equation modeling with factors and composites.
• To provide a statistically and computationally sound alternative to existing PLS-SEM approaches.
• To present the restricted maximum-likelihood approach (RML-SEM) and position SVD-SEM as its initial solution.

Main Methods:

• Development of SVD-SEM, a method based on a non-iterative Singular Value Decomposition (SVD) algorithm.
• Parameter estimation using SVD-SEM yields consistent and asymptotically normal estimators.
• Introduction of RML-SEM for the basic design involving factors and composites.

Main Results:

• SVD-SEM demonstrates superior statistical and computational properties compared to traditional PLS-SEM.
• The SVD-based algorithm ensures convergence and provides reliable parameter estimates.
• Monte Carlo simulations on a nonrecursive model validate the performance of SVD-SEM and RML-SEM.

Conclusions:

• SVD-SEM offers a robust and theoretically grounded alternative for structural equation modeling.
• The proposed methods address critical limitations in existing PLS-SEM techniques.
• SVD-SEM provides a reliable initial solution for RML-SEM, enhancing statistical modeling practices.