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Using Regularization to Identify Measurement Bias Across Multiple Background Characteristics: A Penalized Expectation–Maximization Algorithm

Author

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  • William C. M. Belzak

    (Duolingo Inc.)

  • Daniel J. Bauer

    (University of North Carolina at Chapel Hill)

Abstract

Testing for differential item functioning (DIF) has undergone rapid statistical developments recently. Moderated nonlinear factor analysis (MNLFA) allows for simultaneous testing of DIF among multiple categorical and continuous covariates (e.g., sex, age, ethnicity, etc.), and regularization has shown promising results for identifying DIF among many covariates. However, computationally inefficient estimation methods have hampered practical use of the regularized MNFLA method. We develop a penalized expectation–maximization (EM) algorithm with soft- and firm-thresholding to more efficiently estimate regularized MNLFA parameters. Simulation and empirical results show that, compared to previous implementations of regularized MNFLA, the penalized EM algorithm is faster, more flexible, and more statistically principled. This method also yields similar recovery of DIF relative to previous implementations, suggesting that regularized DIF detection remains a preferred approach over traditional methods of identifying DIF.

Suggested Citation

  • William C. M. Belzak & Daniel J. Bauer, 2024. "Using Regularization to Identify Measurement Bias Across Multiple Background Characteristics: A Penalized Expectation–Maximization Algorithm," Journal of Educational and Behavioral Statistics, , vol. 49(6), pages 976-1012, December.
    • Handle: RePEc:sae:jedbes:v:49:y:2024:i:6:p:976-1012
    DOI: 10.3102/10769986231226439
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