, Volume 43, Issue 4, pp 561–573

A rating formulation for ordered response categories

  • David Andrich

DOI: 10.1007/BF02293814

Cite this article as:
Andrich, D. Psychometrika (1978) 43: 561. doi:10.1007/BF02293814


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.

Key words

logistic latent traitRasch modelthresholdsordered categories

Copyright information

© Psychometric Society 1978

Authors and Affiliations

  • David Andrich
    • 1
  1. 1.Department of EducationThe University of Western AustraliaNedlands