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

Hans Friedrich Köhn; Justin L. Kern

doi:10.1007/978-3-030-01310-3_35

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

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English (US)
Title of host publication	Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018
Editors	Marie Wiberg, Steven Culpepper, Rianne Janssen, Jorge González, Dylan Molenaar
Publisher	Springer
Pages	403-413
Number of pages	11
ISBN (Print)	9783030013097
DOIs	https://doi.org/10.1007/978-3-030-01310-3_35
State	Published - 2019
Event	83rd Annual meeting of the Psychometric Society, 2018 - New York, United States Duration: Jul 9 2018 → Jul 13 2018

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	265
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	83rd Annual meeting of the Psychometric Society, 2018
Country/Territory	United States
City	New York
Period	7/9/18 → 7/13/18

Keywords

Additive trees
Individual differences
Iterative projection
Three-way data

ASJC Scopus subject areas

General Mathematics

Online availability

10.1007/978-3-030-01310-3_35

Library availability

Discover UIUC Full Text

Cite this

Köhn, 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. https://doi.org/10.1007/978-3-030-01310-3_35

Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data. / Köhn, Hans Friedrich ; Kern, Justin L.
Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018. ed. / Marie Wiberg; Steven Culpepper; Rianne Janssen; Jorge González; Dylan Molenaar. Springer, 2019. p. 403-413 (Springer Proceedings in Mathematics and Statistics; Vol. 265).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Köhn, 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, 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

Köhn, Hans Friedrich ; Kern, Justin L. / 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, 2019. pp. 403-413 (Springer Proceedings in Mathematics and Statistics).

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

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Online availability

Library availability

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Quantitative Psychology: 83rd Annual Meeting of the Psychometric Society, New York, NY 2018

Cite this