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Compositional Tables Analysis in Coordinates
Author(s) -
Fačevicová Kamila,
Hron Karel,
Todorov Valentin,
Templ Matthias
Publication year - 2016
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12223
Subject(s) - contingency table , compositional data , mathematics , table (database) , simplex , representation (politics) , column (typography) , euclidean geometry , statistics , combinatorics , geometry , data mining , computer science , connection (principal bundle) , politics , political science , law
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 geometry 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 coordinate 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.