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

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