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Bayesian Adaptive Lasso for Detecting Item-Trait Relationship and Differential Item Functioning in Multidimensional

Na Shan1, Ping-Feng Xu2,3

  • 1School of Psychology & Key Laboratory of Applied Statistics of MOE, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, China. shanna1981@126.com.

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Summary

This study introduces a unified framework to simultaneously detect item-trait relationships and differential item functioning (DIF) in multidimensional item response theory (MIRT) models using a Bayesian adaptive Lasso procedure.

Keywords:
Bayesian adaptive Lassodifferential item functioningitem–trait relationshipmultidimensional item response theory modelregularization

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Area of Science:

  • Psychometrics
  • Statistical modeling
  • Educational measurement

Background:

  • Accurate identification of latent traits is essential in multidimensional tests.
  • Differential item functioning (DIF) is critical for valid group comparisons but often studied separately from item-trait relationships.

Purpose of the Study:

  • To develop a unified framework for detecting both item-trait relationships and DIF within multidimensional item response theory (MIRT) models.
  • To integrate DIF effects into MIRT models as a variable selection problem for latent/observed variables and their interactions.

Main Methods:

  • A Bayesian adaptive Lasso procedure was developed for simultaneous variable selection.
  • This method allows for the concurrent estimation of item-trait relationships and DIF effects.

Main Results:

  • Simulation studies demonstrated the method's effectiveness in parameter estimation.
  • The procedure successfully recovered item-trait relationships and detected DIF effects.

Conclusions:

  • The proposed unified framework and Bayesian adaptive Lasso procedure offer a robust approach for analyzing multidimensional item response data.
  • This method enhances the accuracy of latent trait identification and ensures fairness across different groups by simultaneously addressing item-trait relationships and DIF.