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An exchange algorithm for optimal calibration of items in computerized achievement tests

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  • Ul Hassan, Mahmood
  • Miller, Frank

Abstract

The importance of large scale achievement tests, like national tests in school, eligibility tests for university, or international assessments for evaluation of students, is increasing. Pretesting of questions for the above mentioned tests is done to determine characteristic properties of the questions by adding them to an ordinary achievement test. If computerized tests are used, it has been shown using optimal experimental design methods that it is efficient to assign pretest questions to examinees based on their abilities. The specific distribution of abilities of the available examinees are considered and restricted optimal designs are applied. A new algorithm is developed which builds on an equivalence theorem. It discretizes the design space with the possibility to change the grid adaptively during the run, makes use of an exchange idea and filters computed designs. It is illustrated how the algorithm works through some examples as well as how convergence can be checked. The new algorithm is flexible and can be used even if different models are assumed for different questions.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:157:y:2021:i:c:s0167947321000116
    DOI: 10.1016/j.csda.2021.107177
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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. 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.
    3. 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.
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    8. 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.
    9. 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.
    10. García-Ródenas, Ricardo & García-García, José Carlos & López-Fidalgo, Jesús & Martín-Baos, José Ángel & Wong, Weng Kee, 2020. "A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
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    1. 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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