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The Additive Difference Model and a Metric and an Ordering on Sets

Published online by Cambridge University Press:  01 January 2025

Johannes Becker  and
Werner Pipahl
Johannes Becker*
Affiliation:
University of Duesseldorf
Werner Pipahl
Affiliation:
University of Duesseldorf
*
†Requests for reprints should be sent to J. Becker, University of Duesseldorf, 4 Duesseldorf, Psychologisches Institut II, Moorenstr. 5, Western Germany.
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Abstract

On the basis of the idea of common elements to account for similarity, Restle [1959] developed a set-theoretical model on the generation of similarity judgments. Restle differentiates between his “more qualitative discussion” (p. 207), regarding stimuli as sets of elements and using no geometric concepts or assumptions, and metric quantitative developments of similarity, regarding stimuli as points in a geometric space. To the latter we can count the additive difference model of Beals, Krantz, & Tversky [1968] and Tversky & Krantz [1970].

Despite these differences the two models lead to the same conclusions on the characteristics of similarity judgments.

Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 3 , September 1974 , pp. 361 - 362
Copyright
Copyright © 1974 The Psychometric Society

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Footnotes

*

The authors would like to express their appreciation to Frank Restle for his very helpful comments on parts of this work.

References

Beals, R., Krantz, D. H. and Tversky, A. Foundations of multidimensional scaling. Psychological Review, 1968, 75, 127–142CrossRefGoogle ScholarPubMed
Restle, F. A metric and an ordering on sets. Psychometrika, 1959, 24, 207–220CrossRefGoogle Scholar
Tversky, A. and Krantz, D. H. Similarity of schematic faces: A test of interdimensional additivity. Perception & Psychophysics, 1969, 5, 124–128CrossRefGoogle Scholar
Tversky, A. and Krantz, D. H. The dimensional representation and the metric structure of similarity data. Journal of Mathematical Psychology, 1970, 7, 572–596CrossRefGoogle Scholar
Wender, K. A test of independence of dimensions in multidimensional scaling. Perception & Psychophysics, 1971, 10, 30–32CrossRefGoogle Scholar