Title: Compositional tables with applications in robust statistical analysis: Methodology and computing
Authors: Kamila Facevicova - Palacky University Olomouc (Czech Republic) [presenting]
Karel Hron - Palacky University (Czech Republic)
Valentin Todorov - UNIDO (Austria)
Matthias Templ - Vienna University of Technology (Austria)
Abstract: Compositional tables represent a continuous counterpart to the contingency tables. Accordingly, their cells, containing in general positive real numbers rather than just counts, carry relative information about relationships between two factors. Consequently, compositional tables can be considered as a generalization of (vector) compositional data. Due to relative character of these observations, compositions are popularly expressed in orthonormal coordinates using sequential binary partition (SBP) prior to further processing using standard statistical tools. The contribution presents a general system of orthonormal coordinates with respect to the Aitchison geometry of compositional data, which is constructed as a combination SBPs of whole rows and columns of the table and which enables to analyze interactions between factors in a compositional table. The interpretation of coordinates is closely connected to odds ratios, which are popular also in context of contingency tables. The aim is to apply robust exploratory analysis like outlier detection and PCA including the respective visualization tools to a sample of compositional tables, with a particular focus on proper choice of interpretable orthonormal coordinates and assumptions for the corresponding robust estimators. Computations are performed using comprehensive functions from newly developed R-package on compositional tables.