Uniqueness of real-valued hierarchical classes models

J. Schepers; I. van Mechelen

doi:10.1016/j.jmp.2009.12.006

Uniqueness of real-valued hierarchical classes models

J. Schepers^*, I. van Mechelen

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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 language	English
Pages (from-to)	215-221
Number of pages	7
Journal	Journal of Mathematical Psychology
Volume	54
Issue number	2
DOIs	https://doi.org/10.1016/j.jmp.2009.12.006
Publication status	Published - Apr 2010

Keywords

COMPONENT ANALYSIS
Hierarchical classes
RV-HICLAS
Uniqueness

Access to Document

10.1016/j.jmp.2009.12.006

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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author = "J. Schepers and {van Mechelen}, I.",

year = "2010",

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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

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VL - 54

SP - 215

EP - 221

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

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