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A Rating Formulation for Ordered Response Categories

Published online by Cambridge University Press:  01 January 2025

David Andrich
David Andrich*
Affiliation:
The University of Western Australia
*
Requests for reprints should be sent to David Andrich, Department of Education, The University of Western Australia, NEDLANDS, Western Australia, 6009.
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Abstract

A rating response mechanism for ordered categories, which is related to the traditional threshold formulation but distinctively different from it, is formulated. In addition to the subject and item parameters two other sets of parameters, which can be interpreted in terms of thresholds on a latent continuum and discriminations at the thresholds, are obtained. These parameters are identified with the category coefficients and the scoring function of the Rasch model for polychotomous responses in which the latent trait is assumed uni-dimensional. In the case where the threshold discriminations are equal, the scoring of successive categories by the familiar assignment of successive integers is justified. In the case where distances between thresholds are also equal, a simple pattern of category coefficients is shown to follow.

Keywords

logistic latent traitRasch modelthresholdsordered categories

Information

Type
Original Paper
Information
Psychometrika , Volume 43 , Issue 4 , December 1978 , pp. 561 - 573
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

This work was conducted in part in the first half of 1977 while the author was on study leave at the Danish Institute for Educational Research. The Institute provided required research facilities while The University of Western Australia provided financial support.

References

Reference Notes

Rasch, G. A mathematical theory of objectivity and its consequences for model construction. Paper presented at the European meeting on statistics, econometrics and management science. Amsterdam, 1968.Google Scholar
Andrich, D. Applications of a psychometric model for ordered categories scored with successive integers. Paper presented at the A.E.R.A. Conference, New York, April, 1977.Google Scholar
Kolakowski, D. & Bock, R. D. A Fortran IV program for maximum likelihood item analysis and test scoring: Logistic model for multiple item responses, 1972, Chicago, Ill.: Statistical Laboratory, Department of Education, University of Chicago.Google Scholar
Waller, M. Estimating parameters in the Rasch model: Removing the effects of random guessing, 1976, Princeton, NJ: Educational Testing Service.Google Scholar

References

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