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P. Filzmoser:
"Potentials of compositional data analysis in practical applications";
Talk: CARME 2019, Stellenbosch, Südafrika (invited); 2019-02-04 - 2019-02-06.

Compositional data analysis is not only useful when the values of a multivariate observation sum up to one (constrained data), but also if the main interest of the analysis is in the relationships (ratios) between the variable values. Typical applications include the analysis of geochemical data, data from mass spectroscopy, or, more generally, data that are reported in different categories such as age groups, time windows, regional groups, etc. Typically, the "total" is not relevant, because e.g. the number of employed people in different sectors is not comparable across different countries. We will start with simple pairwise log-ratios to deal with
compositional data, and - in order to avoid over-parametrization with all possible pairs - outline possibilities to construct an orthonormal basis to express this information. Specific choices of such coordinates will support the interpretation of the analysis, and examples for regression and correlation analysis will be shown.
A focus is also on methods which are robust against data outliers. Finally, compositional tables and cubes will be introduced, and their potential will be compared to standard methods.

Compositional data, Coordinates, Robustness, Applications