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Triadic distance models for the analysis of asymmetric three‐way proximity data
Author(s) -
Rooij Mark,
Heiser Willem J.
Publication year - 2000
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711000159204
Subject(s) - asymmetry , categorical variable , representation (politics) , symmetry (geometry) , majorization , mathematics , algorithm , computer science , geometry , combinatorics , statistics , physics , quantum mechanics , politics , political science , law
Triadic distance models can be used to analyse proximity data defined on triples of objects. Three‐way symmetry is a common assumption for triadic distance models. In the present study three‐way symmetry is not assumed. Triadic distance models are presented for the analysis of asymmetric three‐way proximity data that result in a simultaneous representation of symmetry and asymmetry in a low‐dimensional configuration. An iterative majorization algorithm is developed for obtaining the coordinates and the representation of the asymmetry. The models are illustrated by an example using longitudinal categorical data.