Covariance Structure of Compositional Tables

• Main Authors: Kamila Fačevicová, Karel Hron
• Format: Article
• Language: English
• Published: Austrian Statistical Society 2015-10-01
• Series: Austrian Journal of Statistics
• Online Access: http://www.ajs.or.at/index.php/ajs/article/view/80

Recent experiences with interpretation of orthonormal coordinates in compositional data show clearly a necessity of their better understanding in terms of logratios that form the primary source of information within the logratio methodology. This is even more crucial in the special case of compositional tables, where both balances and coordinates with odds ratio interpretation are involved. The aim of the paper is to provide a decompo- sition of covariance structure of orthonormal coordinates in compositional tables in terms of logratio variances that could serve for this purpose. For their better interpretability, the formulas are also accompanied with appropriate comments and graphical illustrations, and implications for the prominent case of 2 2 compositional tables are discussed.