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Non-parametric Regression Among Factor Scores: Motivation and Diagnostics for Nonlinear Structural Equation Models
Steffen Grønneberg1, Julien Patrick Irmer2
1BI Norwegian Business School.
Psychometrika
|February 25, 2026
Summary
This study introduces a framework for analyzing structural equation models, offering new methods to determine functional forms in complex statistical models. Simulation results show improved performance over existing techniques for latent variable analysis.
Area of Science:
- Statistics
- Econometrics
- Psychometrics
Background:
- Structural Equation Models (SEMs) are widely used but determining functional forms can be challenging.
- Confirmatory Factor Analysis (CFA) is a common measurement model, but its structural component requires careful specification.
- Existing methods for diagnosing functional form in SEMs have limitations.
Purpose of the Study:
- To provide a framework for motivating and diagnosing the functional form in the structural part of SEMs.
- To develop theoretically well-founded estimators for conditional expectations of endogenous latent variables.
- To evaluate the performance of these estimators against existing alternatives.
Main Methods:
- Mathematical population-based analysis for asymptotic identification.
- Development of estimators for conditional expectations of latent variables.
- Simulation studies to compare estimator performance.
Main Results:
- The proposed framework successfully addresses functional form specification in SEMs.
- Asymptotic identification results were derived for conditional expectations.
- Simulation studies demonstrated that the new estimators perform well compared to alternatives.
Conclusions:
- The developed framework and estimators offer a valuable tool for structural equation modeling.
- Bartlett factor scores are recommended as input for non-parametric regression methods in practice.
- This research enhances the reliability and validity of SEM analyses.
Keywords:
factor scoresidentificationnon-linear structural equation modelsnon-parametric estimationstructural equation modelsMore Related Videos
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