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A nonspatial methodology for the analysis of two-way proximity data incorporating the distance-density hypothesis

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Abstract

This paper presents a nonspatial operationalization of the Krumhansl (1978, 1982) distancedensity model of similarity. This model assumes that the similarity between two objectsi andj is a function of both the interpoint distance betweeni andj and the density of other stimulus points in the regions surroundingi andj. 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.

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Authors and Affiliations

  1. Marketing and Statistics Departments, graduate School of Business, University of Michigan, 48109-1234, Ann Arbor, MI

    Wayne S. DeSarbo

  2. Marketing Department Wharton School, University of Pennsylvania, USA

    Ajay K. Manrai & Raymond R. Burke

Authors
  1. Wayne S. DeSarbo
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  2. Ajay K. Manrai
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  3. Raymond R. Burke
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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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DeSarbo, W.S., Manrai, A.K. & Burke, R.R. A nonspatial methodology for the analysis of two-way proximity data incorporating the distance-density hypothesis. Psychometrika 55, 229–253 (1990). https://doi.org/10.1007/BF02295285

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  • DOI: https://doi.org/10.1007/BF02295285

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