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Optimal Bayesian Adaptive Design for Test-Item Calibration

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  • Wim Linden
  • Hao Ren

Abstract

An optimal adaptive design for test-item calibration based on Bayesian optimality criteria is presented. The design adapts the choice of field-test items to the examinees taking an operational adaptive test using both the information in the posterior distributions of their ability parameters and the current posterior distributions of the field-test parameters. Different criteria of optimality based on the two types of posterior distributions are possible. The design can be implemented using an MCMC scheme with alternating stages of sampling from the posterior distributions of the test takers’ ability parameters and the parameters of the field-test items while reusing samples from earlier posterior distributions of the other parameters. Results from a simulation study demonstrated the feasibility of the proposed MCMC implementation for operational item calibration. A comparison of performances for different optimality criteria showed faster calibration of substantial numbers of items for the criterion of D-optimality relative to A-optimality, a special case of c-optimality, and random assignment of items to the test takers. Copyright The Psychometric Society 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:2:p:263-288
    DOI: 10.1007/s11336-013-9391-8
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    References listed on IDEAS

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    1. Robert Mislevy & Hua-Hua Chang, 2000. "Does adaptive testing violate local independence?," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 149-156, June.
    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.
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    4. 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.
    5. 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.
    6. 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.
    7. Rosenthal, Jeffrey S., 2007. "AMCMC: An R interface for adaptive MCMC," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5467-5470, August.
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    Cited by:

    1. 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.
    2. 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).
    3. Yinhong He & Ping Chen, 2020. "Optimal Online Calibration Designs for Item Replenishment in Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 85(1), pages 35-55, March.
    4. Wim J. van der Linden & Hao Ren, 2020. "A Fast and Simple Algorithm for Bayesian Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 58-85, February.
    5. Wim J. van der Linden & Bingnan Jiang, 2020. "A Shadow-Test Approach to Adaptive Item Calibration," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 301-321, June.
    6. 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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