TY - GEN

T1 - Additive Trees for Fitting Three-Way (Multiple Source) Proximity Data

AU - Köhn, Hans Friedrich

AU - Kern, Justin L.

N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Additive trees

KW - Individual differences

KW - Iterative projection

KW - Three-way data

UR - http://www.scopus.com/inward/record.url?scp=85066106130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066106130&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-01310-3_35

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

M3 - Conference contribution

AN - SCOPUS:85066106130

SN - 9783030013097

T3 - Springer Proceedings in Mathematics and Statistics

SP - 403

EP - 413

BT - Quantitative Psychology - 83rd Annual Meeting of the Psychometric Society, 2018

A2 - Wiberg, Marie

A2 - Culpepper, Steven

A2 - Janssen, Rianne

A2 - González, Jorge

A2 - Molenaar, Dylan

PB - Springer

T2 - 83rd Annual meeting of the Psychometric Society, 2018

Y2 - 9 July 2018 through 13 July 2018

ER -