Simple enough, but not simpler: reconsidering additive logratio coordinates in compositional analysis

Viktorie Nesrstová ^[2] ; Paulína Jašková ^[2] ; Ivana Pavlů ^[2] ; Karel Hron ^[2] ; Javier Palarea-Albaladejo ^[1] ; Aleš Gába ^[2] ; Jana Pelclová ^[2] ; Kamila Fačevicová ^[2]
1. [1] Universitat de Girona
  
  Universitat de Girona
  
  Gerona, España
2. [2] Palacky University Olomouc
Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 47, Nº. 2, 2023, págs. 31-40
Idioma: inglés
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Resumen
- Compositional data, multivariate observations carrying relative information, are popu- larly expressed in additive logratio coordinates which are easily interpretable as they use one of the components as ratioing part to produce pairwise logratios. These coordi- nates are however oblique and they lead to issues when applying multivariate methods on them, including widely-used techniques such as principal component analysis and linear regression. In this paper we propose a way to redefne alr coordinates with respect to an orthonormal system and we also extend the idea to the case of compositional ta- bles. The new approach is demonstrated in an application to movement behavior data.