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Modeling Model Misspecification in Structural Equation Models

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  • Alexander Robitzsch

    (Centre for International Student Assessment (ZIB), IPN—Leibniz Institute for Science and Mathematics Education, 24118 Kiel, Germany
    Centre for International Student Assessment (ZIB), 24118 Kiel, Germany)

Abstract

Structural equation models constrain mean vectors and covariance matrices and are frequently applied in the social sciences. Frequently, the structural equation model is misspecified to some extent. In many cases, researchers nevertheless intend to work with a misspecified target model of interest. In this article, a simultaneous statistical inference for sampling errors and model misspecification errors is discussed. A modified formula for the variance matrix of the parameter estimate is obtained by imposing a stochastic model for model errors and applying M-estimation theory. The presence of model errors is quantified in increased standard errors in parameter estimates. The proposed inference is illustrated with several analytical examples and an empirical application.

Suggested Citation

  • Alexander Robitzsch, 2023. "Modeling Model Misspecification in Structural Equation Models," Stats, MDPI, vol. 6(2), pages 1-17, June.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:2:p:44-705:d:1171234
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    References listed on IDEAS

    as
    1. Alexander Robitzsch, 2022. "Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches," Stats, MDPI, vol. 5(3), pages 1-42, July.
    2. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    3. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    4. Steven Boker & Michael Neale & Hermine Maes & Michael Wilde & Michael Spiegel & Timothy Brick & Jeffrey Spies & Ryne Estabrook & Sarah Kenny & Timothy Bates & Paras Mehta & John Fox, 2011. "OpenMx: An Open Source Extended Structural Equation Modeling Framework," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 306-317, April.
    5. Rolf Steyer & Erik Sengewald & Sonja Hahn, 2015. "Some Comments on Wu and Browne," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 608-610, September.
    6. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    7. John Hunter, 1968. "Probabilistic foundations for coefficients of generalizability," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 1-18, March.
    8. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    9. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    10. Hao Wu & Michael Browne, 2015. "Quantifying Adventitious Error in a Covariance Structure as a Random Effect," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 571-600, September.
    11. Oberski, Daniel L., 2014. "Evaluating Sensitivity of Parameters of Interest to Measurement Invariance in Latent Variable Models," Political Analysis, Cambridge University Press, vol. 22(1), pages 45-60, January.
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