Multidimensional unfolding by nonmetric multidimensional scaling of Spearman distances in the extended permutation polytope

K. Van Deun, Willem J. Heiser, Luc Delbeke

Research output: Contribution to journalArticleScientificpeer-review

Abstract

A multidimensional unfolding technique that is not prone to degenerate solutions and is based on multidimensional scaling of a complete data matrix is proposed: distance information about the unfolding data and about the distances both among judges and among objects is included in the complete matrix. The latter information is derived from the permutation polytope supplemented with the objects, called the preference sphere. In this sphere, distances are measured that are closely related to Spearman's rank correlation and that are comparable among each other so that an unconditional approach is reasonable. In two simulation studies, it is shown that the proposed technique leads to acceptable recovery of given preference structures. A major practical advantage of this unfolding technique is its relatively easy implementation in existing software for multidimensional scaling.
Original languageEnglish
Pages (from-to)103-132
JournalMultivariate Behavioral Research
Volume42
Issue number1
DOIs
Publication statusPublished - 2007
Externally publishedYes

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Unfolding
Polytope
Permutation
Scaling
Spearman's coefficient
Recovery
Simulation Study
Software
Multidimensional Scaling
Object

Cite this

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abstract = "A multidimensional unfolding technique that is not prone to degenerate solutions and is based on multidimensional scaling of a complete data matrix is proposed: distance information about the unfolding data and about the distances both among judges and among objects is included in the complete matrix. The latter information is derived from the permutation polytope supplemented with the objects, called the preference sphere. In this sphere, distances are measured that are closely related to Spearman's rank correlation and that are comparable among each other so that an unconditional approach is reasonable. In two simulation studies, it is shown that the proposed technique leads to acceptable recovery of given preference structures. A major practical advantage of this unfolding technique is its relatively easy implementation in existing software for multidimensional scaling.",
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Multidimensional unfolding by nonmetric multidimensional scaling of Spearman distances in the extended permutation polytope. / Van Deun, K.; Heiser, Willem J.; Delbeke, Luc.

In: Multivariate Behavioral Research, Vol. 42, No. 1, 2007, p. 103-132.

Research output: Contribution to journalArticleScientificpeer-review

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