### 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) |
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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 New York LLC |

Pages | 403-413 |

Number of pages | 11 |

ISBN (Print) | 9783030013097 |

DOIs | |

State | Published - Jan 1 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 |
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Volume | 265 |

ISSN (Print) | 2194-1009 |

ISSN (Electronic) | 2194-1017 |

### Conference

Conference | 83rd Annual meeting of the Psychometric Society, 2018 |
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Country | United States |

City | New York |

Period | 7/9/18 → 7/13/18 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*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.

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

*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

}

TY - GEN

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

AU - Koehn, Hans Friedrich

AU - Kern, Justin Louis

PY - 2019/1/1

Y1 - 2019/1/1

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

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

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

M3 - Conference contribution

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 New York LLC

ER -