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Interpreting Degenerate Solutions in Unfolding by Use of the Vector Model and the Compensatory Distance Model

Published online by Cambridge University Press:  01 January 2025

K. Van Deun ,
P. J. F. Groenen ,
W. J. Heiser ,
F. M. T. A. Busing  and
L. Delbeke
K. Van Deun*
Affiliation:
Catholic University of Leuven
P. J. F. Groenen
Affiliation:
Erasmus University Rotterdam
W. J. Heiser
Affiliation:
Leiden University
F. M. T. A. Busing
Affiliation:
Leiden University
L. Delbeke
Affiliation:
Catholic University of Leuven
*
Requests for reprints should be sent to K. Van Deun, Department of Psychology, Catholic University of Leuven, Tiensestraat 102, B-3000 Leuven, BELGIUM. E-mail: katrijn.vandeun@psy.kuleuven.ac.be
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Abstract

In this paper, we reconsider the merits of unfolding solutions based on loss functions involving a normalization on the variance per subject. In the literature, solutions based on Stress-2 are often diagnosed to be degenerate in the majority of cases. Here, the focus lies on two frequently occurring types of degeneracies. The first type typically locates some subject points far away from a compact cluster of the other points. In the second type of solution, the object points lie on a circle. In this paper, we argue that these degenerate solutions are well fitting and informative. To reveal the information, we introduce mixtures of plots based on the ideal point model of unfolding, the vector model, and on the signed distance model. In addition to a different representation, we provide a new iterative majorization algorithm to optimize the average squared correlation between the distances in the configuration and the transformed data per individual. It is shown that this approach is equivalent to minimizing Kruskal’s Stress-2.

Keywords

unfoldingdegeneracymixed plotssquared correlationiterative majorization
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 1 , March 2005 , pp. 45 - 69
Copyright
Copyright © 2005 The Psychometric Society

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