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.

This paper presents a new methodology concerned with the estimation of ultrametric trees calibrated on subjects' pairwise proximity judgments of stimuli, capturing subject heterogeneity using a finite mixture formulation. We assume that a number of unobserved classes of subjects exist, each having a different ultrametric tree structure underlying the pairwise proximity judgments. A new likelihood based estimation methodology is presented for those finite mixtures of ultrametric trees, that accommodates ultrametric as well as other external constraints. Various assumptions on the correlation of the error of the dissimilarities are accommodated. The performance of the method to recover known ultrametric tree structures is investigated on synthetic data. An empirical application to published data from Schiffman, Reynolds, and Young (1981) is provided. The ability to deal with external constraints on the tree-topology is demonstrated, and a comparison with an alternative clustering based method is made.