Behaviormetrika
Online ISSN : 1349-6964
Print ISSN : 0385-7417
ISSN-L : 0385-7417
MULTIDIMENSIONAL SCALING OF ASYMMETRIC PROXIMITY: MODEL AND METHOD
Takayuki SaitoShin-ichi Takeda
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1990 Volume 17 Issue 28 Pages 49-80

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Abstract

This paper proposes a mutidimensional scaling method for asymmetric proximity data whose diagonal entries are not all equal. For a suggested model, necessary and sufficient conditions and algebraic solutions are presented. The method consisting of two algorithms is developed, which gives multidimensional configuration, unidimensional scale of any psychological quantities and the degree of asymmetry of the data. The quantities should be interpreted through data analysis or examined with any hypothesis. A simulation study using artificial data demonstrates that the method works successfully, showing sufficient robustness and capability to recover the original structure. Illustrative applications are presented. Extensions of the model are argued, and properties of the model and the algorithms are discussed with another simulation study.

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© The Behaviormetric Society of Japan
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