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Defining asymmetry in item response theory.

Leah M Feuerstahler1, Jay Verkuilen2, Fabio Setti1

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Summary
This summary is machine-generated.

Asymmetric item response theory (asymIRT) offers a more accurate way to model test responses than traditional methods. This study unifies definitions and introduces new measures for quantifying item asymmetry in IRT models.

Keywords:
item analysisitem response theorypsychometrics

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Area of Science:

  • Psychometrics
  • Educational Measurement
  • Item Response Theory

Background:

  • Classical item response theory (IRT) often relies on symmetric item response functions (IRFs), which may not accurately reflect real-world response patterns.
  • Existing asymmetric item response theory (asymIRT) models lack a unified framework for definition, interpretation, and quantification of asymmetry.
  • Ambiguity exists regarding the precise definition of asymmetry and the relationships between different asymmetric IRT models.

Purpose of the Study:

  • To provide a unified framework for defining, interpreting, and measuring asymmetry in IRT models.
  • To propose general definitions of IRF symmetry based on the first derivative of the IRF.
  • To introduce practical quantile-based measures for quantifying item asymmetry.

Main Methods:

  • Refined Samejima's notion of point symmetry to develop general IRF symmetry definitions.
  • Utilized properties of the first derivative of the IRF for defining symmetry.
  • Introduced quantile-based measures of skewness to quantify item asymmetry.

Main Results:

  • Clarified the status of various IRT models (e.g., 3PL, unipolar, asymmetric functions) within the proposed framework.
  • Demonstrated the behavior of quantile-based skewness measures across different asymmetric models.
  • Showed that item asymmetry significantly impacts latent trait estimation, affecting how items penalize or reward responses.

Conclusions:

  • Asymmetry is a fundamental item characteristic in IRT, comparable to difficulty and discrimination.
  • The proposed framework and measures offer practical tools for comparing asymIRT models.
  • This work enhances the understanding of substantive implications of item asymmetry in educational and psychological measurement.