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Optimal Item Difficulty for the Three-Parameter Normal Ogive Response Model

Published online by Cambridge University Press:  01 January 2025

John H. Wolfe
John H. Wolfe*
Affiliation:
Navy Personnel Research And Development Center
*
Requests for reprints should be sent to J. H. Wolfe, Navy Personnel Research and Development Center, San Diego, Ca 92152.
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Abstract

In tailored testing, it is important to determine the optimal difficulty of the next item to present to the examinee. This paper shows that the difference that maximizes information for the three-parameter normal ogive response model is approximately 1.7 times the optimal difference θ − b for the three-parameter logistic model. Under the normal model, calculation of the optimal difficulty for minimizing the Bayes risk is equivalent to maximizing an associated information function.

Keywords

item difficultyitem response theorylatent trait theoryitem analysis
Type
Notes And Comments
Information
Psychometrika , Volume 46 , Issue 4 , December 1981 , pp. 461 - 464
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

The views expressed herein, are those of the author and do not necessarily reflect those of the Department of the Navy.

References

Reference Notes

Owen, R. J. Bayesian sequential design and analysis of dichotomous experiments with special reference to mental testing, 1970, Ann Arbor: University of Michigan.Google Scholar
Vale, C. D. & Weiss, D. J. A rapid item-search procedure for Bayesian adaptive testing. Research Report 77-4, Psychometric Methods Program, University of Minnesota, May 1977.CrossRefGoogle Scholar

References

Birnbaum, A. 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, 1968, Reading, MA: Addison-Wesley.Google Scholar
Lord, F. M. Applications of item response theory to practical testing problems, 1980, Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
Owen, R. J. A bayesian sequential procedure for quantal response in the context of adaptive mental testing. Journal of the American Statistical Association, 1975, 70, 351–356.CrossRefGoogle Scholar