Working with compositional data in coordinates

Compositional data are multivariate observations carrying only relative information, popularly expressed in percentages, proportions, mg/kg, etc. Because of features inherent to compositional data, such as scale invariance and the relative scale, the statistical analysis of raw compositional data often leads to spurious results. Natural principles of compositional data are followed by the Aitchison geometry on a simplex, the sample space of compositional data (Aitchison, 1986; Pawlowsky-Glahn et al., 2015). However, because most standard statistical methods rely on the Euclidean geometry in real space, compositional data need to be converted to this space prior to statistical processing. In the lecture, we will present the log ratio methodology for dealing with compositional data and several types of their coordinate representations, such as orthonormal log-ratio coordinates, pivot coordinates, weighted pivot coordinates (Hron et al., 2017), or symmetric balances (!
Kynvclova et al., 2017). Their usage will be demonstrated on examples.