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Does Adaptive Testing Violate Local Independence?

Published online by Cambridge University Press:  01 January 2025

Robert J. Mislevy  and
Hua-Hua Chang
Robert J. Mislevy*
Affiliation:
Educational Testing Service
Hua-Hua Chang
Affiliation:
The National Board of Medical Examiners
*
Requests for reprints should be sent to Robert Mislevy, Educational Testing Service, Princeton, NJ 08541. E-mail: [email protected].
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Abstract

Item response theory posits “local independence,” or conditional independence of item responses given item parameters and examinee proficiency parameters. The usual definition of local independence, however, addresses the context of fixed tests, and initially appears to yield incorrect response-pattern probabilities in the context of adaptive testing. The paradox is resolved by introducing additional notation to deal with the item selection mechanism.

Keywords

adaptive testingconditional independenceitem response theory (IRT)local independence
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 2 , June 2000 , pp. 149 - 156
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

We are grateful to Charlie Lewis, Ming-Mei Wang, and Pao-Kuei Wu for discussions on this topic, and to the Editor, the reviewers, and Howard Wainer for helpful comments on an earlier version of the paper. The first author's work was supported in part by the National Center for Research on Evaluation, Standards, Student Testing (CRESST), Educational Research and Development Program, cooperative agreement number R117G10027 and CFDA catalog number 84.117G, as administered by the Office of Educational Research and Improvement, U.S. Department of Education.

References

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F.M., & Novick, M.R. (Eds.), Statistical theories of mental test scores. Reading, MA: Addison-Wesley.Google Scholar
Chang, H., & Ying, Z. (in press). Nonlinear sequential designs for logistic item response theory models, with applications to computerized adaptive tests. Annals of Statistics.Google Scholar
Lord, F.M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Erlbaum.Google Scholar
Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.Google Scholar
Mislevy, R.J., & Wu, P.-K. (1996). Missing responses and Bayesian IRT ability estimation: Omits, choice, time limits, and adaptive testing. Princeton, NJ: Educational Testing Service.Google Scholar
Owen, R.J. (1975). A Bayesian sequential procedure for quantal response in the context of adaptive mental testing. Journal of the American Statistical Association, 70, 351–356.CrossRefGoogle Scholar
Rubin, D.B. (1976). Inference and missing data. Biometrika, 63, 581–592.CrossRefGoogle Scholar
Wainer, H., Dorans, N.J., Flaugher, R., Green, B.F., Mislevy, R.J., Steinberg, L., & Thissen, D. (1990). Computerized adaptive testing: A primer. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar