Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Additive trees are graph-theoretic models that can be used for constructing network representations of pairwise proximity data observed on a set of N objects. Each object is represented as a terminal node in a connected graph; the length of the paths connecting the nodes reflects the inter-object proximities. Carroll, Clark, and DeSarbo (J Classif 1:25–74, 1984) developed the INDTREES algorithm for fitting additive trees to analyze individual differences of proximity data collected from multiple sources. INDTREES is a mathematical programming algorithm that uses a conjugate gradient strategy for minimizing a least-squares loss function augmented by a penalty term to account for violations of the constraints as imposed by the underlying tree model. This article presents an alternative method for fitting additive trees to three-way two-mode proximity data that does not rely on gradient-based optimization nor on penalty terms, but uses an iterative projection algorithm. A real-world data set consisting of 22 proximity matrices illustrated that the proposed method gave virtually identical results as the INDTREES method.

Original languageEnglish (US)
Title of host publicationQuantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018
EditorsMarie Wiberg, Steven Culpepper, Rianne Janssen, Jorge González, Dylan Molenaar
Number of pages11
ISBN (Print)9783030013097
StatePublished - 2019
Event83rd Annual meeting of the Psychometric Society, 2018 - New York, United States
Duration: Jul 9 2018Jul 13 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017


Conference83rd Annual meeting of the Psychometric Society, 2018
Country/TerritoryUnited States
CityNew York


  • Additive trees
  • Individual differences
  • Iterative projection
  • Three-way data

ASJC Scopus subject areas

  • General Mathematics


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