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Spatial, Non-Spatial and Hybrid Models for Scaling

Published online by Cambridge University Press:  01 January 2025

J. Douglas Carroll
J. Douglas Carroll*
Affiliation:
Bell Laboratories
*
Requests for reprints should be sent to Dr. J. Douglas Carroll, Bell Laboratories, Murray Hill, New Jersey 07974.
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Abstract

In this paper, hierarchical and non-hierarchical tree structures are proposed as models of similarity data. Trees are viewed as intermediate between multidimensional scaling and simple clustering. Procedures are discussed for fitting both types of trees to data. The concept of multiple tree structures shows great promise for analyzing more complex data. Hybrid models in which multiple trees and other discrete structures are combined with continuous dimensions are discussed. Examples of the use of multiple tree structures and hybrid models are given. Extensions to the analysis of individual differences are suggested.

Keywords

multidimensional scalinghierarchical tree structuresclusteringgeometric modelsmultivariate data analysis
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 4 , December 1976 , pp. 439 - 463
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

1976 Psychometric Society Presidential Address.

While people too numerous to list here have contributed ideas, inspiration, and other help, I particularly wish to acknowledge the contributions of Sandra Pruzansky, without whom this paper could not have been written. I would also like to acknowledge the past contributions of my long-time colleague Jih-Jie Chang, without whose help I probably would not have been asked to write it.

References

Reference Notes

Carroll, J. D., and Pruzansky, S. Fitting of hierarchical tree structure (HTS) models, mixtures of HTS models, and hybrid models, via mathematical programming and alternating least squares. Presented at the U.S.-Japan Seminar on Theory, Methods, and Applications of Multidimensional Scaling and related techniques, San Diego, Aug. 1975. Paper in informally published Proceedings of U.S.-Japan Seminar, available on request.Google Scholar
Cunningham, J. P. On finding an optimal tree realization of a proximity matrix. Paper presented at the Mathematical Psychology meeting, Ann Arbor, Michigan, August 29, 1974.Google Scholar
Harshman, R. A. PARAFAC2: Mathematical and technical notes, 1972, Los Angeles: University of California.Google Scholar
Kruskal, Joseph B. Some advances in parametric mapping. Psychometric Society Presidential Address, presented at joint meeting of Psychometric Society and Classification Society, Iowa City, Iowa, April, 1975.Google Scholar
Sattath, S. and Tversky, A. Additive similarity trees. Unpublished manuscript, Hebrew University, 1976.Google Scholar
Shepard, R. N. and Arabie, P. Additive cluster analysis of similarity data. Paper presented at the U.S.-Japan Seminar on Theory, Methods, and Applications of Multidimensional Scaling and Related Techniques, San Diego, 1975. Paper in informally published Proceedings of U.S.-Japan Seminar.Google Scholar
Tversky, A. Features of similarity, 1976, Jerusalem, Israel: Hebrew University.Google Scholar

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