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Optimal Item Calibration for Computerized Achievement Tests

Author

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  • Mahmood Ul Hassan

    (Stockholm University)

  • Frank Miller

    (Stockholm University)

Abstract

Item calibration is a technique to estimate characteristics of questions (called items) for achievement tests. In computerized tests, item calibration is an important tool for maintaining, updating and developing new items for an item bank. To efficiently sample examinees with specific ability levels for this calibration, we use optimal design theory assuming that the probability to answer correctly follows an item response model. Locally optimal unrestricted designs have usually a few design points for ability. In practice, it is hard to sample examinees from a population with these specific ability levels due to unavailability or limited availability of examinees. To counter this problem, we use the concept of optimal restricted designs and show that this concept naturally fits to item calibration. We prove an equivalence theorem needed to verify optimality of a design. Locally optimal restricted designs provide intervals of ability levels for optimal calibration of an item. When assuming a two-parameter logistic model, several scenarios with D-optimal restricted designs are presented for calibration of a single item and simultaneous calibration of several items. These scenarios show that the naive way to sample examinees around unrestricted design points is not optimal.

Suggested Citation

  • Mahmood Ul Hassan & Frank Miller, 2019. "Optimal Item Calibration for Computerized Achievement Tests," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1101-1128, December.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:4:d:10.1007_s11336-019-09673-6
    DOI: 10.1007/s11336-019-09673-6
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    References listed on IDEAS

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    1. Hung-Yi Lu, 2014. "Application of Optimal Designs to Item Calibration," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-8, September.
    2. Martijn Berger, 1992. "Sequential sampling designs for the two-parameter item response theory model," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 521-538, December.
    3. Wim Linden & Hao Ren, 2015. "Optimal Bayesian Adaptive Design for Test-Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 263-288, June.
    4. Hao Ren & Wim J. van der Linden & Qi Diao, 2017. "Continuous Online Item Calibration: Parameter Recovery and Item Utilization," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 498-522, June.
    5. Martijn Berger & C. Joy King & Weng Wong, 2000. "Minimax d-optimal designs for item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 377-390, September.
    6. Douglas Jones & Zhiying Jin, 1994. "Optimal sequential designs for on-line item estimation," Psychometrika, Springer;The Psychometric Society, vol. 59(1), pages 59-75, March.
    7. Yuan-chin Chang & Hung-Yi Lu, 2010. "Online Calibration Via Variable Length Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 140-157, March.
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    Cited by:

    1. Ul Hassan, Mahmood & Miller, Frank, 2021. "An exchange algorithm for optimal calibration of items in computerized achievement tests," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    2. Frank Miller & Ellinor Fackle-Fornius, 2024. "Parallel Optimal Calibration of Mixed-Format Items for Achievement Tests," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 903-928, September.

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