Purposeful weighting of components in geochemical (compositional) data

For varied reasons, in practical analysis of geochemical (compositional) data we are often interested in adjusting the role or the influence of variables on the final results. For instance, a measuring device used to analyse the chemical mixture of soil samples might not necessarily have the same accuracy for all components, particularly for those with low concentrations. This can have a severe impact on results and interpretation of popular methods like principal component analysis, regression analysis or clustering, but also on the quality of imputation of values below detection limit of a measurement device. In all these cases, a sensible weighting scheme for the variables would generally lead to a statistical analysis better reflecting the underlying phenomenon of interest and less influenced by some limitations or issues with the data collection process. In addition, the relative nature of geochemical data (i.e., those in units like mg/kg, proportions or percentages), where the relevant information is contained in ratios between components, needs to be taken into account for a reliable statistical processing. In this contribution we propose a sensible way of weighting of geochemical components using a generalisation of the logratio methodology for compositional data analysis, namely, the Bayes space approach. We provide practical examples of such weighting and also highlight that the Bayes space approach enables one to develop a methodological framework where it is possibly to apply any weighting strategy in a controlled way.