Subcompositional coherence and and a novel proportionality index of parts
Egozcue, Juan José (Universidad Politecnica de Catalunya. Departament d'Enginyeria Civil i Ambiental)
Pawlowsky-Glahn, Vera (Universitat de Girona. Departament d'Informàtica, Matemàtica Aplicada i Estadística)

Date:	2023
Abstract:	Research in compositional data analysis was motivated by spurious (Pearson) correlation. Spurious results are due to semantic incoherence, but the question of ways to relate parts in a statistically consistent way remains open. To solve this problem, we first define a coherent system of functions with respect to a subcomposition and analyze the space of parts. This leads to understanding why measures like covariance and correlation depend on the subcomposition considered, while measures like the distance between parts are independent of the same. It allows the definition of a novel index of proportionality between parts.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Compositional data analysis ; Aitchison geometry ; Simplex ; Compositional parts ; Proportionality ; Dominance ; Correlation
Published in:	SORT : statistics and operations research transactions, Vol. 47 Núm. 2 (2023) , p. 229-244, ISSN 2013-8830

Adreça original: https://raco.cat/index.php/SORT/article/view/421903
DOI: 10.57645/20.8080.02.7

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