an:06659001
Zbl 1373.62338
Fa??evicov??, Kamila; Hron, Karel; Todorov, Valentin; Templ, Matthias
Compositional tables analysis in coordinates
EN
Scand. J. Stat. 43, No. 4, 962-977 (2016).
00360998
2016
j
62H99 62H17 62H25
Aitchison geometry on the simplex; balances; compositional data; contingency tables; isometric log-ratio transformation
Summary: 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.