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Wald χ2 Test for Differential Item Functioning Detection with Polytomous Items in Multilevel Data.

Sijia Huang1, Dubravka Svetina Valdivia1

  • 1Indiana University Bloomington, USA.

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Summary

This study introduces a new method for detecting differential item functioning (DIF) in multilevel assessments with polytomous items. The approach effectively identifies biased items, ensuring fairer testing for all participants.

Keywords:
Wald χ2 testdifferential item functioningitem response theorymeasurement invariancemultilevel data

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Statistics

Background:

  • Equitable measurement in assessments requires identifying differential item functioning (DIF).
  • Detecting DIF in multilevel data structures presents a significant challenge not fully addressed by existing methods.
  • Polytomous items, common in many assessments, add complexity to DIF analysis.

Purpose of the Study:

  • To introduce a novel procedure for detecting uniform and non-uniform DIF in polytomous items within multilevel data.
  • To extend existing two-stage DIF detection procedures to accommodate multilevel data structures.

Main Methods:

  • A Lord's Wald chi-squared test-based procedure was developed for DIF detection.
  • The Metropolis-Hastings Robbins-Monro (MH-RM) algorithm was employed for estimating multilevel polytomous item response theory (IRT) models and covariance matrices.
  • A two-stage approach was utilized, involving anchor item identification followed by candidate item evaluation.

Main Results:

  • The proposed approach demonstrated high power in identifying DIF items.
  • The method effectively controlled the Type I error rate in simulation studies.
  • The procedure is robust under various simulated conditions mimicking real-world data.

Conclusions:

  • The developed procedure offers a powerful and reliable method for detecting DIF in polytomous items within multilevel assessment data.
  • This advancement contributes to more equitable measurement by providing tools to identify and address item bias in complex data structures.
  • Further research should explore additional conditions and applications of this multilevel DIF detection method.