Hostname: page-component-6bf8c574d5-qdpjg Total loading time: 0 Render date: 2025-02-17T14:07:56.811Z Has data issue: false hasContentIssue false

A Rating Formulation for Ordered Response Categories

Published online by Cambridge University Press:  01 January 2025

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.

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.

Type
Original Paper
Copyright
Copyright © 1978 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

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

Andersen, E. B. Conditional inference for multiple-choice questionnaires. British Journal of Mathematical and Statistical Psychology, 1973, 26, 3144.CrossRefGoogle Scholar
Andersen, E. B. Sufficient statistics and latent trait models. Psychometrika, 1977, 42, 6981.CrossRefGoogle Scholar
Birnbaum, A. Some latent trait models and their use in inferring an examinee's ability. In Lord, F. & Novick, M. (Eds.), Statistical theories of mental test scores, 1968, Reading: Mass. Addison-Wesley.Google Scholar
Lord, F. A theory of test scores. Psychometric Monograph, 7, 1952.Google Scholar
Lumsden, J. Person reliability. Applied Psychological Measurement, 1977, 4, 477482.CrossRefGoogle Scholar
Rasch, G. On general laws and the meaning of measurement in psychology. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press. 1961, 321–34.Google Scholar
Samejima, F. Estimation of latent ability using a response pattern of graded scores. Psychometric Monograph, 1969, 34 (2, Whole No. 17).Google Scholar