CUSUM-Based Person-Fit Statistics for Adaptive Testing

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

Journal of Educational and Behavioral Statistics, 2001, vol. 26, issue 2, 199-217

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.

Keywords: appropriateness measurement; computer adaptive testing; cumulative sum; item response theory; person fit (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:26:y:2001:i:2:p:199-217

DOI: 10.3102/10769986026002199

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