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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

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