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

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

Abstract

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
PublisherSpringer New York LLC
Pages403-413
Number of pages11
ISBN (Print)9783030013097
DOIs
StatePublished - Jan 1 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
Volume265
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference83rd Annual meeting of the Psychometric Society, 2018
CountryUnited States
CityNew York
Period7/9/187/13/18

Fingerprint

Proximity
Penalty
Square Functions
Individual Differences
Projection Algorithm
Conjugate Gradient
Term
Loss Function
Vertex of a graph
Mathematical Programming
Iterative Algorithm
Least Squares
Connected graph
Pairwise
Gradient
Path
Optimization
Alternatives
Graph in graph theory
Model

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Koehn, H. F., & Kern, J. L. (2019). Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data. In M. Wiberg, S. Culpepper, R. Janssen, J. González, & D. Molenaar (Eds.), Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018 (pp. 403-413). (Springer Proceedings in Mathematics and Statistics; Vol. 265). Springer New York LLC. https://doi.org/10.1007/978-3-030-01310-3_35

Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data. / Koehn, Hans Friedrich; Kern, Justin Louis.

Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. ed. / Marie Wiberg; Steven Culpepper; Rianne Janssen; Jorge González; Dylan Molenaar. Springer New York LLC, 2019. p. 403-413 (Springer Proceedings in Mathematics and Statistics; Vol. 265).

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

Koehn, HF & Kern, JL 2019, Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data. in M Wiberg, S Culpepper, R Janssen, J González & D Molenaar (eds), Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. Springer Proceedings in Mathematics and Statistics, vol. 265, Springer New York LLC, pp. 403-413, 83rd Annual meeting of the Psychometric Society, 2018, New York, United States, 7/9/18. https://doi.org/10.1007/978-3-030-01310-3_35
Koehn HF, Kern JL. Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data. In Wiberg M, Culpepper S, Janssen R, González J, Molenaar D, editors, Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. Springer New York LLC. 2019. p. 403-413. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-030-01310-3_35
Koehn, Hans Friedrich ; Kern, Justin Louis. / Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data. Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. editor / Marie Wiberg ; Steven Culpepper ; Rianne Janssen ; Jorge González ; Dylan Molenaar. Springer New York LLC, 2019. pp. 403-413 (Springer Proceedings in Mathematics and Statistics).
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