Non-parametric Regression Among Factor Scores: Motivation and Diagnostics for Nonlinear Structural Equation Models

Area of Science:

• Statistics
• Econometrics
• Psychometrics

Background:

• Structural Equation Models (SEMs) are widely used for analyzing complex relationships between observed and latent variables.
• Accurately specifying the functional form in the structural part of SEMs is crucial for valid inference.
• Existing methods may lack robustness or theoretical grounding for diagnosing functional form misspecification.

Purpose of the Study:

• To propose a novel framework for motivating and diagnosing the functional form in SEMs.
• To address misspecification in the structural component when the measurement model is a linear confirmatory factor model.
• To provide theoretically sound estimators for conditional expectations of endogenous latent variables.

Main Methods:

• Mathematical population-based analysis to derive asymptotic identification results.
• Development of theoretically well-founded estimators for conditional expectations.
• Simulation studies to evaluate the performance of the proposed estimators against alternatives.
• Application of Bartlett factor scores with non-parametric regression methods.

Main Results:

• Asymptotic identification results for conditional expectations were established.
• The proposed estimators demonstrated favorable performance in simulation studies compared to existing methods.
• The framework effectively aids in diagnosing functional form misspecification in SEMs.

Conclusions:

• The developed framework provides a robust approach to functional form specification in SEMs.
• The recommended estimator using Bartlett factor scores offers a practical and effective solution.
• This research contributes to more reliable analysis of latent variable models.