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A Geometrical Analysis of the Unfolding Model: General Solutions

Published online by Cambridge University Press:  01 January 2025

John Davidson
John Davidson*
Affiliation:
The University of Tasmania
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Abstract

Given the complete set R of rank orders obtained from any configuration of n stimulus points in r dimensions in accordance with the unfolding model, a configuration from which just these orders may be derived will be described as a solution for R. The space is assumed to be Euclidean. Necessary and sufficient conditions are derived for a configuration to be a solution for R. The geometrical constraints which are necessary and sufficient to determine the subset of pairs of orders and opposites contained in R are also identified and constitute the constraint system for the ordinal vector model. The relationship between the two models is discussed.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 3 , September 1973 , pp. 305 - 336
Copyright
Copyright © 1973 The Psychometric Society

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