Hostname: page-component-5f745c7db-q8b2h Total loading time: 0 Render date: 2025-01-06T06:38:51.621Z Has data issue: true hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.CrossRefGoogle Scholar
Andrich, D. (1982). An extension of the Rasch model for ratings providing both location and dispersion parameters. Psychometrika, 47, 105–113.CrossRefGoogle Scholar
Birnbaum, A. (1968). 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 (pp. 395–479). Reading, MA: Addison-Wesley.Google Scholar
Huynh, H. (1994). On equivalence between a partial credit item and a set of independent Rasch binary items. Psychometrika, 59, 111–119.CrossRefGoogle Scholar
Huynh, H. (1996). Decomposition of a Rasch partial credit item into independent binary and indecomposable trinary items. Psychometrika, 61, 31–39.CrossRefGoogle Scholar
Lord, F. M. (1980). Applications of item response theory to practical testing problems, Hillsdale, NY: Lawrence Erlbaum.Google Scholar
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.CrossRefGoogle Scholar
Mislevy, R., Johnson, E., Muraki, E. (1992). Scaling procedures in NAEP. Journal of Educational Statistics, 17, 131–154.Google Scholar
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.CrossRefGoogle Scholar
Muraki, E. (1993). Information functions of the generalized partial credit model. Applied Psychological Measurement, 17, 351–363.CrossRefGoogle Scholar
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests, Copenhagen: Danish Institute for Educational Research.Google Scholar