IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v6y2023i2p44-705d1171234.html

Modeling Model Misspecification in Structural Equation Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/6/2/44/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/6/2/44/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Alexander Robitzsch, 2023. "Linking Error in the 2PL Model," J, MDPI, vol. 6(1), pages 1-27, January.
    4. William Meredith, 1993. "Measurement invariance, factor analysis and factorial invariance," Psychometrika, Springer;The Psychometric Society, vol. 58(4), pages 525-543, December.
    5. John Hunter, 1968. "Probabilistic foundations for coefficients of generalizability," Psychometrika, Springer;The Psychometric Society, vol. 33(1), pages 1-18, March.
    6. Rosseel, Yves, 2012. "lavaan: An R Package for Structural Equation Modeling," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i02).
    7. 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.
    8. 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.
    9. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    10. 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.
    11. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Keke Lai, 2019. "Creating Misspecified Models in Moment Structure Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 781-801, September.
    3. Edgar Merkle & Achim Zeileis, 2013. "Tests of Measurement Invariance Without Subgroups: A Generalization of Classical Methods," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 59-82, January.
    4. Alexander Robitzsch, 2020. "L p Loss Functions in Invariance Alignment and Haberman Linking with Few or Many Groups," Stats, MDPI, vol. 3(3), pages 1-38, August.
    5. Johan Oud & Manuel Voelkle, 2014. "Do missing values exist? Incomplete data handling in cross-national longitudinal studies by means of continuous time modeling," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3271-3288, November.
    6. Becker Bettina & Theuringer Martin, 2001. "Macroeconomic Determinants of Contingent Protection: The Case of the European Union," Zeitschrift für Wirtschaftspolitik, De Gruyter, vol. 50(3), pages 350-374, December.
    7. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    8. Barone-Adesi, Giovanni & Fusari, Nicola & Mira, Antonietta & Sala, Carlo, 2020. "Option market trading activity and the estimation of the pricing kernel: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 216(2), pages 430-449.
    9. Agostino Capponi & Zhaonan Qu, 2025. "Handling Sparse Non-negative Data in Finance," Papers 2509.01478, arXiv.org.
    10. Gary King, 1989. "A Seemingly Unrelated Poisson Regression Model," Sociological Methods & Research, , vol. 17(3), pages 235-255, February.
    11. Emilie Alberola & Benoît Chèze & Julien Chevallier, 2008. "The EU Emissions Trading Scheme : Disentangling the Effects of Industrial Production and CO2 Emissions on Carbon Prices," EconomiX Working Papers 2008-12, University of Paris Nanterre, EconomiX.
    12. Hao Wu & Michael Browne, 2015. "Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 619-624, September.
    13. Blazsek, Szabolcs & Escribano, Álvaro & Licht, Adrian, 2018. "Seasonal quasi-vector autoregressive models for macroeconomic data," UC3M Working papers. Economics 26316, Universidad Carlos III de Madrid. Departamento de Economía.
    14. Stefan Boes & Michael Gerfin, 2016. "Does Full Insurance Increase the Demand for Health Care?," Health Economics, John Wiley & Sons, Ltd., vol. 25(11), pages 1483-1496, November.
    15. Gurmu, Shiferaw & Rilstone, Paul & Stern, Steven, 1998. "Semiparametric estimation of count regression models1," Journal of Econometrics, Elsevier, vol. 88(1), pages 123-150, November.
    16. Pang, Arwin, 2017. "Incorporating the effect of successfully bagging big game into recreational hunting: An examination of deer, moose and elk hunting," Journal of Forest Economics, Elsevier, vol. 28(C), pages 12-17.
    17. Cassiman, Bruno & Veugelers, Reinhilde & Arts, Sam, 2018. "Mind the gap: Capturing value from basic research through combining mobile inventors and partnerships," Research Policy, Elsevier, vol. 47(9), pages 1811-1824.
    18. La Vecchia, Davide & Camponovo, Lorenzo & Ferrari, Davide, 2015. "Robust heart rate variability analysis by generalized entropy minimization," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 137-151.
    19. Cui, Xin & Wen, Lulu & Wang, Chunfeng & Fang, Zhenming & Yao, Shouyu, 2025. "Innovating under pressure: How geopolitical risk exposure drives energy innovation in firms," Energy Economics, Elsevier, vol. 148(C).
    20. Hajivassiliou, Vassilis A. & Ruud, Paul A., 1986. "Classical estimation methods for LDV models using simulation," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 40, pages 2383-2441, Elsevier.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jstats:v:6:y:2023:i:2:p:44-705:d:1171234. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.