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A Geometrical Analysis of the Unfolding Model: Nondegenerate Solutions

Published online by Cambridge University Press:  01 January 2025

J. A. Davidson
J. A. Davidson*
Affiliation:
The University of Newcastle
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Abstract

Given the complete set R of rank orders derived from some configuration of n stimulus points in r dimensions in accordance with the unfolding model, a stimulus configuration which generates just these orders will be described as a solution for R. The space is assumed to be Euclidean. Necessary and sufficient conditions are determined for a nondegenerate configuration to be a solution for R. The geometrical conditions which are necessary and sufficient to determine the subset of pairs of opposite orders are also identified and constitute the constraint system for the ordinal vector model.

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 2 , June 1972 , pp. 193 - 216
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

The present work was completed while the writer was in receipt of an Australian Commonwealth Postgraduate Scholarship under the supervision of Professor J. A. Keats.

†

Now at the University of Tasmania, Hobart, Australia.

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