Defining asymmetry in item response theory.

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.