Uniqueness of real-valued hierarchical classes models

J. Schepers, I. van Mechelen

Research output: Contribution to journalArticleAcademicpeer-review

3 Citations (Scopus)

Abstract

Two novel uniqueness theorems are derived for the family of hierarchical classes (HICLAS) models, a family of structural decomposition models for N-way N-mode data that imply simultaneous hierarchically organized classifications of all modes involved in the data. The theorems generalize earlier results on binary HICLAS models to the integer- and real-valued cases. In addition, they allow for a shorter and insightful proof of a result on Boolean matrix invertibility that goes back to earlier work of Luce (1952) and Rutherford (1963). 

Original languageEnglish
Pages (from-to)215-221
Number of pages7
JournalJournal of Mathematical Psychology
Volume54
Issue number2
DOIs
Publication statusPublished - Apr 2010

Keywords

  • COMPONENT ANALYSIS
  • Hierarchical classes
  • RV-HICLAS
  • Uniqueness

Cite this

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abstract = "Two novel uniqueness theorems are derived for the family of hierarchical classes (HICLAS) models, a family of structural decomposition models for N-way N-mode data that imply simultaneous hierarchically organized classifications of all modes involved in the data. The theorems generalize earlier results on binary HICLAS models to the integer- and real-valued cases. In addition, they allow for a shorter and insightful proof of a result on Boolean matrix invertibility that goes back to earlier work of Luce (1952) and Rutherford (1963). ",
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Uniqueness of real-valued hierarchical classes models. / Schepers, J.; van Mechelen, I.

In: Journal of Mathematical Psychology, Vol. 54, No. 2, 04.2010, p. 215-221.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

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AU - Schepers, J.

AU - van Mechelen, I.

PY - 2010/4

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N2 - Two novel uniqueness theorems are derived for the family of hierarchical classes (HICLAS) models, a family of structural decomposition models for N-way N-mode data that imply simultaneous hierarchically organized classifications of all modes involved in the data. The theorems generalize earlier results on binary HICLAS models to the integer- and real-valued cases. In addition, they allow for a shorter and insightful proof of a result on Boolean matrix invertibility that goes back to earlier work of Luce (1952) and Rutherford (1963). 

AB - Two novel uniqueness theorems are derived for the family of hierarchical classes (HICLAS) models, a family of structural decomposition models for N-way N-mode data that imply simultaneous hierarchically organized classifications of all modes involved in the data. The theorems generalize earlier results on binary HICLAS models to the integer- and real-valued cases. In addition, they allow for a shorter and insightful proof of a result on Boolean matrix invertibility that goes back to earlier work of Luce (1952) and Rutherford (1963). 

KW - COMPONENT ANALYSIS

KW - Hierarchical classes

KW - RV-HICLAS

KW - Uniqueness

U2 - 10.1016/j.jmp.2009.12.006

DO - 10.1016/j.jmp.2009.12.006

M3 - Article

VL - 54

SP - 215

EP - 221

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

SN - 0022-2496

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ER -