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Differential Item Functioning Analysis Without A Priori Information on Anchor Items: QQ Plots and Graphical Test

Author

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  • Ke-Hai Yuan

    (University of Notre Dame)

  • Hongyun Liu

    (Beijing Normal University)

  • Yuting Han

    (Beijing Normal University)

Abstract

Differential item functioning (DIF) analysis is an important step in establishing the validity of measurements. Most traditional methods for DIF analysis use an item-by-item strategy via anchor items that are assumed DIF-free. If anchor items are flawed, these methods will yield misleading results due to biased scales. In this article, based on the fact that the item’s relative change of difficulty difference (RCD) does not depend on the mean ability of individual groups, a new DIF detection method (RCD-DIF) is proposed by comparing the observed differences against those with simulated data that are known DIF-free. The RCD-DIF method consists of a D-QQ (quantile quantile) plot that permits the identification of internal references points (similar to anchor items), a RCD-QQ plot that facilitates visual examination of DIF, and a RCD graphical test that synchronizes DIF analysis at the test level with that at the item level via confidence intervals on individual items. The RCD procedure visually reveals the overall pattern of DIF in the test and the size of DIF for each item and is expected to work properly even when the majority of the items possess DIF and the DIF pattern is unbalanced. Results of two simulation studies indicate that the RCD graphical test has Type I error rate comparable to those of existing methods but with greater power.

Suggested Citation

  • Ke-Hai Yuan & Hongyun Liu & Yuting Han, 2021. "Differential Item Functioning Analysis Without A Priori Information on Anchor Items: QQ Plots and Graphical Test," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 345-377, June.
    • Handle: RePEc:spr:psycho:v:86:y:2021:i:2:d:10.1007_s11336-021-09746-5
    DOI: 10.1007/s11336-021-09746-5
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    References listed on IDEAS

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    1. Gerhard Tutz & Moritz Berger, 2016. "Item-focussed Trees for the Identification of Items in Differential Item Functioning," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 727-750, September.
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    Cited by:

    1. Chen, Yunxiao & Li, Chengcheng & Ouyang, Jing & Xu, Gongjun, 2023. "DIF statistical inference without knowing anchoring items," LSE Research Online Documents on Economics 119923, London School of Economics and Political Science, LSE Library.
    2. Wallin, Gabriel & Chen, Yunxiao & Moustaki, Irini, 2024. "DIF analysis with unknown groups and anchor items," LSE Research Online Documents on Economics 121991, London School of Economics and Political Science, LSE Library.
    3. Peter F. Halpin, 2024. "Differential Item Functioning via Robust Scaling," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 796-821, September.
    4. Paul Boeck & Sun-Joo Cho, 2021. "Not all DIF is shaped similarly," Psychometrika, Springer;The Psychometric Society, vol. 86(3), pages 712-716, September.

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