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Estimating Structural Equation Models Using James–Stein Type Shrinkage Estimators

Published online by Cambridge University Press:  01 January 2025

Elissa Burghgraeve Open the ORCID record for Elissa Burghgraeve [Opens in a new window] ,
Jan De Neve Open the ORCID record for Jan De Neve [Opens in a new window]  and
Yves Rosseel Open the ORCID record for Yves Rosseel [Opens in a new window]
Elissa Burghgraeve*
Affiliation:
Ghent University
Jan De Neve
Affiliation:
Ghent University
Yves Rosseel
Affiliation:
Ghent University
*
Correspondence should be made to Elissa Burghgraeve, Department of Data Analysis, Ghent University, Henri Dunantlaan 1, Ghent, Belgium. Email: Elissa.Burghgraeve@UGent.be
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Abstract

We propose a two-step procedure to estimate structural equation models (SEMs). In a first step, the latent variable is replaced by its conditional expectation given the observed data. This conditional expectation is estimated using a James–Stein type shrinkage estimator. The second step consists of regressing the dependent variables on this shrinkage estimator. In addition to linear SEMs, we also derive shrinkage estimators to estimate polynomials. We empirically demonstrate the feasibility of the proposed method via simulation and contrast the proposed estimator with ML and MIIV estimators under a limited number of simulation scenarios. We illustrate the method on a case study.

Keywords

regression calibrationmeasurement errorshrinkage estimator
Type
Theory and Methods
Information
Psychometrika , Volume 86 , Issue 1 , March 2021 , pp. 96 - 130
Copyright
Copyright © 2021 The Psychometric Society

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