Modeling Model Misspecification in Structural Equation Models

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

Stats, 2023, vol. 6, issue 2, 1-17

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.

Keywords: model misspecification; model error; structural equation modeling; M-estimation (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2023
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