The estimation of ultrametric and path length trees from rectangular proximity data

Geert De Soete, Wayne Desarbo, George W. Furnas, J. Douglas Carroll

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Abstract

A least-squares algorithm for fitting ultrametric and path length or additive trees to two-way, two-mode proximity data is presented. The algorithm utilizes a penalty function to enforce the ultrametric inequality generalized for asymmetric, and generally rectangular (rather than square) proximity matrices in estimating an ultrametric tree. This stage is used in an alternating least-squares fashion with closed-form formulas for estimating path length constants for deriving path length trees. The algorithm is evaluated via two Monte Carlo studies. Examples of fitting ultrametric and path length trees are presented.

Original languageEnglish (US)
Pages (from-to)289-310
Number of pages22
JournalPsychometrika
Volume49
Issue number3
DOIs
Publication statusPublished - Sep 1 1984

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All Science Journal Classification (ASJC) codes

  • Psychology(all)
  • Applied Mathematics

Cite this

De Soete, G., Desarbo, W., Furnas, G. W., & Carroll, J. D. (1984). The estimation of ultrametric and path length trees from rectangular proximity data. Psychometrika, 49(3), 289-310. https://doi.org/10.1007/BF02306021