Mixtures of (constrained) ultrametric trees

Michel Wedel, Wayne Desarbo

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)419-443
Number of pages25
JournalPsychometrika
Volume63
Issue number4
DOIs
StatePublished - Jan 1 1998

Fingerprint

Finite Mixture
Tree Structure
Aptitude
Proximity
Topology
Pairwise
Cluster Analysis
Methodology
Dissimilarity
Synthetic Data
Likelihood
Clustering
Formulation
Alternatives
Judgment
Class

All Science Journal Classification (ASJC) codes

  • Psychology(all)
  • Applied Mathematics

Cite this

Wedel, Michel ; Desarbo, Wayne. / Mixtures of (constrained) ultrametric trees. In: Psychometrika. 1998 ; Vol. 63, No. 4. pp. 419-443.
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Wedel, M & Desarbo, W 1998, 'Mixtures of (constrained) ultrametric trees', Psychometrika, vol. 63, no. 4, pp. 419-443. https://doi.org/10.1007/BF02294863

Mixtures of (constrained) ultrametric trees. / Wedel, Michel; Desarbo, Wayne.

In: Psychometrika, Vol. 63, No. 4, 01.01.1998, p. 419-443.

Research output: Contribution to journalArticle

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