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A Nonspatial Methodology for the Analysis of Two-Way Proximity Data Incorporating the Distance-Density Hypothesis

Published online by Cambridge University Press:  01 January 2025

Wayne S. DeSarbo ,
Ajay K. Manrai  and
Raymond R. Burke
Wayne S. DeSarbo*
Affiliation:
Marketing and Statistics Departments, University of Michigan
Ajay K. Manrai
Affiliation:
Marketing Department, Wharton School, University of Pennsylvania
Raymond R. Burke
Affiliation:
Marketing Department, Wharton School, University of Pennsylvania
*
Requests for reprints should be sent to Wayne S. DeSarbo, Marketing and Statistics Departments, Graduate School of Business, University of Michigan, Ann Arbor, MI 48109-1234.
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Abstract

This paper presents a nonspatial operationalization of the Krumhansl (1978, 1982) distance-density model of similarity. This model assumes that the similarity between two objects i and j is a function of both the interpoint distance between i and j and the density of other stimulus points in the regions surrounding i and j. We review this conceptual model and associated empirical evidence for such a specification. A nonspatial, tree-fitting methodology is described which is sufficiently flexible to fit a number of competing hypotheses of similarity formation. A sequential, unconstrained minimization algorithm is technically presented together with various program options. Three applications are provided which demonstrate the flexibility of the methodology. Finally, extensions to spatial models, three-way analyses, and hybrid models are discussed.

Keywords

asymmetric similarityultrametric treeshierarchical clusteringKrumbansl's distance-density model
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 2 , June 1990 , pp. 229 - 253
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

The authors wish to thank three anonymous reviewers and the editor for their insightful comments on a previous draft of this manuscript.

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