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Estimating Structural Equation Models Using James-Stein Type Shrinkage Estimators.

Elissa Burghgraeve1, Jan De Neve2, Yves Rosseel2

  • 1Department of Data Analysis, GHENT UNIVERSITY, Henri Dunantlaan 1, Ghent, Belgium. Elissa.Burghgraeve@UGent.be.

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Summary
This summary is machine-generated.

This study introduces a novel two-step method for estimating structural equation models (SEMs) using shrinkage estimators for latent variables. The approach enhances model estimation accuracy, particularly for polynomial SEMs.

Keywords:
measurement errorregression calibrationshrinkage estimator

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Area of Science:

  • Statistics
  • Econometrics
  • Psychometrics

Background:

  • Structural Equation Models (SEMs) are widely used for analyzing complex relationships between observed and latent variables.
  • Traditional SEM estimation methods can be sensitive to model misspecification and data characteristics.
  • There is a need for robust and efficient estimation techniques for SEMs.

Purpose of the Study:

  • To propose a novel two-step estimation procedure for SEMs.
  • To develop shrinkage estimators for latent variables in both linear and polynomial SEMs.
  • To evaluate the performance of the proposed method against existing estimators.

Main Methods:

  • A two-step estimation procedure is introduced.
  • The first step involves estimating the latent variable's conditional expectation using a James-Stein type shrinkage estimator.
  • The second step regresses dependent variables on the estimated latent variable.

Main Results:

  • The proposed method demonstrates feasibility through simulation studies.
  • Shrinkage estimators are derived for both linear and polynomial SEMs.
  • The performance is contrasted with Maximum Likelihood (ML) and Multiple Indicator, Multiple Instrumental Variable (MIIV) estimators.

Conclusions:

  • The proposed shrinkage-based method offers a viable alternative for SEM estimation.
  • The method shows promise for handling complex SEMs, including polynomial forms.
  • Empirical illustration on a case study validates the practical applicability of the technique.