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

Psychometrika, Volume 55, Issue 2, pp 229-253, 1990

25 Pages Posted: 2 Jun 2016

See all articles by Wayne S. DeSarbo

Wayne S. DeSarbo

Pennsylvania State University

Ajay K Manrai

University of Delaware

Raymond R. Burke

University of Pennsylvania - The Wharton School

Date Written: June 1990

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 similarity, ultrametric trees, hierarchical clustering, Krumbansl's distance-density model

Suggested Citation

DeSarbo, Wayne S. and Manrai, Ajay K and Burke, Raymond R., A Nonspatial Methodology for the Analysis of Two-Way Proximity Data Incorporating the Distance-Density Hypothesis (June 1990). Psychometrika, Volume 55, Issue 2, pp 229-253, 1990. Available at SSRN: https://ssrn.com/abstract=2787243

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

Ajay K Manrai

University of Delaware ( email )

214 MBNA America Hall
Orchard Road & Amstel Avenue
Newark, DE 19716-2710
United States
302-831-1770 (Phone)
302-831-4196 (Fax)

Raymond R. Burke

University of Pennsylvania - The Wharton School ( email )

3641 Locust Walk
Philadelphia, PA 19104-6365
United States

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