Title: Compositional tables and their coordinate representations
Authors: Karel Hron - Palacky University (Czech Republic) [presenting]
Kamila Facevicova - Palacky University Olomouc (Czech Republic)
Julie Rendlova - Palacky University (Czech Republic)
Abstract: A data table which is arranged according to two factors can be considered as a compositional table if the relative structure of the relationship between factors is of primary interest. An example is the total amount of unemployed people, split according to gender and age classes. Analyzed as a compositional table, the relevant information would consist of ratios between different cells of such a table. This perspective is particularly useful when analyzing several compositional tables jointly, where the absolute scale of observations may differ substantially, e.g. if unemployment data are considered from different countries. Within the framework of the logratio methodology, compositional tables can be decomposed into independent and interactive parts, and real orthonormal coordinates that enable statistical processing using standard multivariate methods can be assigned to these parts. The aim is to review recent developments on compositional tables, particularly to construct such orthonormal coordinates that make it possible to decompose the table. As an alternative, coefficients with respect to a generating system (centered logratio coefficients), that are frequently preferred in the logratio methodology due to easy interpretability, will be discussed. Finally, also an outlook to the multi-factorial case will be outlined.