Compositional Tables Analysis in Coordinates
本文提出用Aitchison几何替代标准欧氏几何来分析成分表，将表格分解为独立部分和交互部分，并找到可解释的坐标表示，应用于健康调查和宏观经济数据。
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 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.