Compositional tables analysis in coordinates

Abstract

Compositional tables – a continuous counterpart to the contingency tables – carry relative information about relationships between row and column factors; thus, for their analysis, only ratios between cells of a table are informative. Consequently, the standard Euclidean geome- try should be replaced by the Aitchison geometry on the simplex that enables decomposition of the table into its independent and interactive parts. The aim of the paper is to find interpretable coordi- nate representation for independent and interaction tables (in sense of balances and odds ratios of cells, respectively), where further statistical processing of compositional tables can be performed. Theoretical results are applied to real-world problems from a health survey and in macroeconomics.