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Item Information and Discrimination Functions for Trinary PCM Items

Published online by Cambridge University Press:  01 January 2025

Wies Akkermans  and
Eiji Muraki
Wies Akkermans*
Affiliation:
University of Twente
Eiji Muraki
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to W. Akkermans, University of Twente, Department of Education, P.O. Box 217, 7500 AlE ENSCHEDE, THE NETHERLANDS.
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Abstract

For trinary partial credit items the shape of the item information and the item discrimination function is examined in relation to the item parameters. In particular, it is shown that these functions are unimodal if δ2 − δ1 < 4 ln 2 and bimodal otherwise The locations and values of the maxima are derived. Furthermore, it is demonstrated that the value of the maximum is decreasing in δ2 − δ1. Consequently, the maximum of a unimodal item information function is always larger than the maximum of a bimodal one, and similarly for the item discrimination function.

Keywords

partial credit modeltrinary itemsitem information functionitem discrimination functionmaximum item information
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 4 , December 1997 , pp. 569 - 578
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

The work reported herein was partially supported under the National Assessment of Educational Progress (Grant No. R999G30002; CFDA No. 84.999G) as administered by the Office of Educational Research and Improvement, US Department of Education.

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