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.
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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.
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.
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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.
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Andrich, D. A rating formulation for ordered response categories. Psychometrika 43, 561–573 (1978). https://doi.org/10.1007/BF02293814
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DOI: https://doi.org/10.1007/BF02293814