Covariance Structure of Compositional Tables (Austrian Journal of Statistics, 2015)
Recent experiences with interpretation of orthonormal coordinates in compositionaldata show clearly a necessity of their better understanding in terms of logratios that formthe primary source of information within the logratio methodology. This is even morecrucial in the special case of compositional tables, where both balances and coordinateswith 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 termsof 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.