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

Steffen Grønneberg () and Julien Patrick Irmer ()
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Steffen Grønneberg: BI Norwegian Business School
Julien Patrick Irmer: Goethe University Frankfurt

Psychometrika, 2024, vol. 89, issue 3, No 5, 822-850

Abstract: Abstract We provide a framework for motivating and diagnosing the functional form in the structural part of nonlinear or linear structural equation models when the measurement model is a correctly specified linear confirmatory factor model. A mathematical population-based analysis provides asymptotic identification results for conditional expectations of a coordinate of an endogenous latent variable given exogenous and possibly other endogenous latent variables, and theoretically well-founded estimates of this conditional expectation are suggested. Simulation studies show that these estimators behave well compared to presently available alternatives. Practically, we recommend the estimator using Bartlett factor scores as input to classical non-parametric regression methods.

Keywords: structural equation models; non-linear structural equation models; non-parametric estimation; identification; factor scores (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11336-024-09959-4

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