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.
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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 theU.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.
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Tversky, A. Features of similarity. Unpublished manuscript, Hebrew University, Jerusalem, Israel, 1976.
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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 beenasked to write it.
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Carroll, J.D. Spatial, non-spatial and hybrid models for scaling. Psychometrika 41, 439–463 (1976). https://doi.org/10.1007/BF02296969
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DOI: https://doi.org/10.1007/BF02296969