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Distractor Selection Ratios

Published online by Cambridge University Press:  01 January 2025

Thomas E. Love
Thomas E. Love*
Affiliation:
Department of Operations Research, Weatherhead School of Management, Case Western Reserve University
*
Requests for reprints should be sent to Thomas E. Love, Department of Operations Research, Weatherhead School of Management, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106-7235.
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Abstract

A latent variable representation for multiple-choice item and option characteristic curves is presented. Under standard assumptions of conditional independence of item responses and monotonicity of item characteristic curves, a criterion for distractors is proposed based on distractor selection ratios. A connection is made between the proposed criterion and the theory of individual choice behavior, providing new insight. The main results allow for the testing of the criterion from observable data without first specifying a parametric form for the characteristic curves. A series of examples apply the method.

Keywords

item response theorymultiple-choice itemslatent variable modelsindividual choice behaviorassociationcontingency tables

Information

Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 1 , March 1997 , pp. 51 - 62
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

The author gratefully acknowledges Paul R. Rosenbaum for valuable conversations on the subject of this paper, as well as David Hildebrand and Abba Krieger for their comments and encouragement at a presentation on this subject which led to improvements in the paper. This work was supported in part by a grant from the Department of Statistics at the University of Pennsylvania, for which the author thanks Paul Shaman. Finally, he thanks three anonymous referees for their valuable comments.

References

Birch, M. W. (1964). The detection of partial association, I: The 2×2 case. Journal of the Royal Statistical Society, Series B, 26, 313–324.CrossRefGoogle Scholar
Birch, M. W. (1965). The detection of partial association, II: The general case. Journal of the Royal Statistical Society, Series B, 27, 111–124.CrossRefGoogle Scholar
Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51.CrossRefGoogle Scholar
Fienberg, S. E. (1979). Log linear representation for paired comparison models with ties and within-pair order effects. Biometrics, 35, 479–481.CrossRefGoogle Scholar
Fienberg, S. E. (1980). The analysis of cross-classified categorical data, Cambridge, MA: MIT Press.Google Scholar
Fienberg, S. E., Larntz, K. (1976). Loglinear representation for paired and multiple comparisons models. Biometrika, 63, 245–254.CrossRefGoogle Scholar
Goodman, L. A., Kruskal, W. H. (1979). Measures of association for cross classifications, New York: Springer-Verlag.CrossRefGoogle Scholar
Holland, P. W. (1981). When are item response models consistent with observed data?. Psychometrika, 46, 79–92.CrossRefGoogle Scholar
Holland, P. W., Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent variable models. Annals of Statistics, 14, 1523–1543.CrossRefGoogle Scholar
Junker, B. W. (1991). Essential independence and likelihood-based ability estimation for polytomous items. Psychometrika, 56, 255–278.CrossRefGoogle Scholar
Levine, M. V., Drasgow, F. (1983). The relation between incorrect option choice and estimated proficiency. Educational and Psychological Measurement, 43, 675–685.CrossRefGoogle Scholar
Luce, R. D. (1959). Individual choice behavior, New York: Wiley.Google Scholar
Mantel, N. (1963). Chi-square tests with one degree of freedom; extensions of the Mantel-Haenszel procedure. Journal of the American Statistical Association, 58, 690–700.Google Scholar
Mantel, N., Haenszel, W. (1959). Statistical aspects of the retrospective study of disease. Journal of the National Cancer Institute, 22, 719–748.Google ScholarPubMed
Mislevy, R. J., Verhelst, N. (1990). Modeling item responses when different subjects employ different solutions strategies. Psychometrika, 55, 195–216.CrossRefGoogle Scholar
Rosenbaum, P. R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory. Psychometrika, 49, 425–435.CrossRefGoogle Scholar
Rosenbaum, P. R. (1987). Comparing item characteristic curves. Psychometrika, 52, 217–233.CrossRefGoogle Scholar
Samejima, F. (1979). A new family of models for the multiple choice item, Knoxville: University of Tennessee, Department of Psychology.CrossRefGoogle Scholar
Thissen, D., Steinberg, L. (1984). A response model for multiple choice items. Psychometrika, 49, 501–519.CrossRefGoogle Scholar