Mixtures of (Constrained) Ultrametric Trees

Psychometrika, Volume 63, Issue 4, pp 419-443

Posted: 11 Jun 2016

See all articles by Michel Wedel

Michel Wedel

University of Maryland - Robert H. Smith School of Business, Marketing Department; University of Groningen - Faculty of Economics and Business

Wayne S. DeSarbo

Pennsylvania State University

Date Written: December 1998

Abstract

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.

Keywords: hierarchical clustering, finite mixtures, ultrametric trees, maximum likelihood, constrained estimation, latent class analysis

Suggested Citation

Wedel, Michel and DeSarbo, Wayne S., Mixtures of (Constrained) Ultrametric Trees (December 1998). Psychometrika, Volume 63, Issue 4, pp 419-443. Available at SSRN: https://ssrn.com/abstract=2792321

Michel Wedel

University of Maryland - Robert H. Smith School of Business, Marketing Department ( email )

College Park, MD 20742
United States
301.405.2162 (Phone)
301.405.0146 (Fax)

HOME PAGE: http://www.rhsmith.umd.edu/marketing/faculty/wedel.html

University of Groningen - Faculty of Economics and Business ( email )

Postbus 72
9700 AB Groningen
Netherlands

Wayne S. DeSarbo (Contact Author)

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

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