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Mixtures of (Constrained) Ultrametric Trees

Published online by Cambridge University Press:  01 January 2025

Michel Wedel  and
Wayne S. DeSarbo
Michel Wedel*
Affiliation:
University of Groningen
Wayne S. DeSarbo
Affiliation:
Pennsylvania State University
*
Requests for reprints should be send to: Michel Wedel, Faculty of Economics, University of Groningen, PO Box 800, 9700 AV Groningen, THE NETHERLANDS.
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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 clusteringfinite mixturesultrametric treesmaximum likelihoodconstrained estimationlatent class analysis
Type
Original Paper
Information
Psychometrika , Volume 63 , Issue 4 , December 1998 , pp. 419 - 443
Copyright
Copyright © 1998 The Psychometric Society

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Footnotes

The authors wish to thank the Editor, Associate Editor, and two anonymous reviewers for their excellent comments and suggestions which helped improve the manuscript.

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