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CUSUM-Based Person-Fit Statistics for Adaptive Testing

Author

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  • Edith M.L.A. van Krimpen-Stoop
  • Rob R. Meijer

Abstract

Item scores that do not fit an assumed item response theory model may cause the latent trait value to be inaccurately estimated. Several person-fit statistics for detecting nonfitting score patterns for paper-and-pencil tests have been proposed. In the context of computerized adaptive tests (CAT), the use of person-fit analysis has hardly been explored. Because it has been shown that the distribution of existing person-fit statistics is not applicable in a CAT, in this study new person-fit statistics are proposed and critical values for these statistics are derived from existing statistical theory. Statistics are proposed that are sensitive to runs of correct or incorrect item scores and are based on all items administered in a CAT or based on subsets of items, using observed and expected item scores and using cumulative sum (CUSUM) procedures. The theoretical and empirical distributions of the statistics are compared and detection rates are investigated. Results showed that the nominal and empirical Type I error rates were comparable for CUSUM procedures when the number of items in each subset and the number of measurement points were not too small. Detection rates of CUSUM procedures were superior to other fit statis­tics. Applications of the statistics are discussed.

Suggested Citation

  • Edith M.L.A. van Krimpen-Stoop & Rob R. Meijer, 2001. "CUSUM-Based Person-Fit Statistics for Adaptive Testing," Journal of Educational and Behavioral Statistics, , vol. 26(2), pages 199-217, June.
    • Handle: RePEc:sae:jedbes:v:26:y:2001:i:2:p:199-217
    DOI: 10.3102/10769986026002199
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    Cited by:

    1. Edison M. Choe & Jinming Zhang & Hua-Hua Chang, 2018. "Sequential Detection of Compromised Items Using Response Times in Computerized Adaptive Testing," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 650-673, September.
    2. Tendeiro, Jorge N. & Meijer, Rob R. & Niessen, A. Susan M., 2016. "PerFit: An R Package for Person-Fit Analysis in IRT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i05).

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