Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model

K. Van Deun, P. J. F. Groenen, W. J. Heiser, F. M. T. A. Busing, L. Delbeke

Research output: Contribution to journalArticleScientificpeer-review

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: unfolding, degeneracy, mixed plots, squared correlation, iterative majorization
Original languageEnglish
Pages (from-to)45-69
JournalPsychometrika
Volume70
Issue number1
DOIs
Publication statusPublished - 2005
Externally publishedYes

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Unfolding
Majorization
Farthest Point
Loss Function
Signed
Degeneracy
Normalization
Circle
Optimise
Model
Configuration

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Van Deun, K. ; Groenen, P. J. F. ; Heiser, W. J. ; Busing, F. M. T. A. ; Delbeke, L. / Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model. In: Psychometrika. 2005 ; Vol. 70, No. 1. pp. 45-69.
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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: unfolding, degeneracy, mixed plots, squared correlation, iterative majorization",
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Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model. / Van Deun, K. ; Groenen, P. J. F.; Heiser, W. J.; Busing, F. M. T. A.; Delbeke, L.

In: Psychometrika, Vol. 70, No. 1, 2005, p. 45-69.

Research output: Contribution to journalArticleScientificpeer-review

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