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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.