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A Comment on Birnbaum’s Three-Parameter Logistic Model in the Latent Trait Theory

Published online by Cambridge University Press:  01 January 2025

Fumiko Samejima
Fumiko Samejima*
Affiliation:
Bowling Green State University
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Abstract

Birnbaum's three-parameter logistic model for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. It is clarified that with models of knowledge or random guessing nature, which include the three-parameter logistic model, the unique maximum condition is not satisfied for the correct answer, and the item response information function is negative for the interval (− ∞, θg). It is suggested that we should use θg as a criterion in selecting optimal items for a specified group of examinees, so that we can practically avoid the possibility of non-unique maxima of the likelihood function on the response pattern given by an examinee in the group.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 2 , June 1973 , pp. 221 - 233
Copyright
Copyright © 1973 The Psychometric Society

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Footnotes

*

The work described in this paper was partially done while ehe author was at University of New Brunswick, Canada, in 1968-1970, supported by NRC Grant APA-345 from National Research Council of Canada.

References

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