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

Viktorie Nesrstová, Paulína Jašková, Ivana Pavlů, Karel Hron, Javier Palarea Albaladejo, Aleš Gába, Jana Pelclová, Kamila Facevicová

• 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.