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Estimating Structural Equation Models Using James–Stein Type Shrinkage Estimators

Author

Listed:
  • Elissa Burghgraeve

    (GHENT UNIVERSITY)

  • Jan De Neve

    (GHENT UNIVERSITY)

  • Yves Rosseel

    (GHENT UNIVERSITY)

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.

Suggested Citation

  • Elissa Burghgraeve & Jan De Neve & Yves Rosseel, 2021. "Estimating Structural Equation Models Using James–Stein Type Shrinkage Estimators," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 96-130, March.
    • Handle: RePEc:spr:psycho:v:86:y:2021:i:1:d:10.1007_s11336-021-09749-2
    DOI: 10.1007/s11336-021-09749-2
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    References listed on IDEAS

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    1. Kenneth Bollen, 1996. "An alternative two stage least squares (2SLS) estimator for latent variable equations," Psychometrika, Springer;The Psychometric Society, vol. 61(1), pages 109-121, March.
    2. repec:ucp:bkecon:9780226316529 is not listed on IDEAS
    3. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    4. Yutaka Kano, 1990. "Noniterative estimation and the choice of the number of factors in exploratory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 55(2), pages 277-291, June.
    5. P. Bentler, 1968. "Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 33(3), pages 335-345, September.
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