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A New Interpretation of Stochastic Test Models

Published online by Cambridge University Press:  01 January 2025

Hans Colonius
Hans Colonius*
Affiliation:
Technische Universität Braunschweig
*
Requests for reprints should be sent to Hans Colonius, Technische Universität Braurtschweig, Spielmannstrasse 19, D-3300 Braunschweig, Federal Republic of Germany.
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Abstract

A new look at latent trait models is proposed. The event of an item being solved by a person is related to the event that the momentary value of a person-specific random component is at least as large as the corresponding value of an item-specific random component. The Birnbaum logistic test model is shown to be generated by a bivariate extreme value distribution for the components. Some consequences of this interpretation are outlined.

Keywords

logistic test modelextreme value distributionitem discriminating power

Information

Type
Notes And Comments
Information
Psychometrika , Volume 46 , Issue 2 , June 1981 , pp. 223 - 225
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

I am indebted to David Strauss for calling the extreme value distribution (1) to my attention in a random utility context. The paper also benefited from discussions with H. C. Micko, H. H. Schulze and K. F. Wender.

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, Mass.: Addison-Wesley.Google Scholar
de Oliveira, J. T. La représentation des distributions extrêmales bivariées. Bulletin of the International Statistical Institute, 1961, 33, 477–480.Google Scholar
Johnson, N. L. & Kotz, S. Distributions in statistics: Continuous multivariate distributions, 1972, New York: Wiley.Google Scholar
Luce, R. D. & Suppes, P. Preference, utility and subjective probability. In Luce, R. D., Bush, R. R. & Galanter, E. (Eds.), Handbook of Mathematical Psychology (Vol. III), 1965, New York: Wiley.Google Scholar
Rasch, G. Probabilistic models for some intelligence and attainment tests, 1960, Copenhagen: Nielson & Lydiche.Google Scholar
Strauss, D. Some results on random utility models. Journal of Mathematical Psychology, 1979, 20, 35–52.CrossRefGoogle Scholar
Yellott, J. I. The relationship between Luce's choice axiom, Thurstone's theory of comparative judgment, and the double exponential distribution. Journal of Mathematical Psychology, 1977, 15, 109–144.CrossRefGoogle Scholar