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Online Calibration of a Joint Model of Item Responses and Response Times in Computerized Adaptive Testing

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  • Hyeon-Ah Kang

    (University of Texas at Austin)

  • Yi Zheng

    (Arizona State University)

  • Hua-Hua Chang

    (Purdue University)

Abstract

With the widespread use of computers in modern assessment, online calibration has become increasingly popular as a way of replenishing an item pool. The present study discusses online calibration strategies for a joint model of responses and response times. The study proposes likelihood inference methods for item paramter estimation and evaluates their performance along with optimal sampling procedures. An extensive simulation study indicates that the proposed online calibration strategies perform well with relatively small samples (e.g., 500∼800 examinees). The analysis of estimated parameters suggests that response time information can be used to improve the recovery of the response model parameters. Among a number of sampling methods investigated, A -optimal sampling was found most advantageous when the item parameters were weakly correlated. When the parameters were strongly correlated, D -optimal sampling tended to achieve the most accurate parameter recovery. The study provides guidelines for deciding sampling design under a specific goal of online calibration given the characteristics of field-testing items.

Suggested Citation

  • Hyeon-Ah Kang & Yi Zheng & Hua-Hua Chang, 2020. "Online Calibration of a Joint Model of Item Responses and Response Times in Computerized Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 45(2), pages 175-208, April.
    • Handle: RePEc:sae:jedbes:v:45:y:2020:i:2:p:175-208
    DOI: 10.3102/1076998619879040
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    References listed on IDEAS

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    1. Jochen Ranger & Jorg-Tobias Kuhn, 2012. "A flexible latent trait model for response times in tests," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 31-47, January.
    2. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    3. 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.
    4. Ping Chen & Tao Xin & Chun Wang & Hua-Hua Chang, 2012. "Online Calibration Methods for the DINA Model with Independent Attributes in CD-CAT," Psychometrika, Springer;The Psychometric Society, vol. 77(2), pages 201-222, April.
    5. Wim Linden & Edith Krimpen-Stoop, 2003. "Using response times to detect aberrant responses in computerized adaptive testing," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 251-265, June.
    6. Wim Linden & Fanmin Guo, 2008. "Bayesian Procedures for Identifying Aberrant Response-Time Patterns in Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 73(3), pages 365-384, September.
    7. Wim Linden & Cees Glas, 2010. "Statistical Tests of Conditional Independence Between Responses and/or Response Times on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 120-139, March.
    8. Wim van der Linden, 2007. "A Hierarchical Framework for Modeling Speed and Accuracy on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 287-308, September.
    9. Jochen Ranger, 2013. "A Note on the Hierarchical Model for Responses and Response Times in Tests of van der Linden (2007)," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 538-544, July.
    10. Ping Chen & Chun Wang, 2016. "A New Online Calibration Method for Multidimensional Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 674-701, September.
    11. Joris Mulder & Wim Linden, 2009. "Multidimensional Adaptive Testing with Optimal Design Criteria for Item Selection," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 273-296, June.
    12. 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.
    13. 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.
    14. 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.
    15. Fox, Jean-Paul & Entink, Rinke Klein & van der Linden, Wilm, 2007. "Modeling of Responses and Response Times with the Package cirt," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i07).
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    Cited by:

    1. Hyeon-Ah Kang, 2023. "Sequential Generalized Likelihood Ratio Tests for Online Item Monitoring," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 672-696, June.

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