Publications in Scientific Journals:
K. Facevicova, K. Hron, V. Todorov, M. Templ:
"General approach to coordinate representation of compositional tables";
Scandinavian Journal of Statistics,
45
(2018),
4;
879
- 899.
English abstract:
Compositional tables can be considered a continuous counterpart to the well‐known contingency tables. Their cells, which generally contain positive real numbers rather than just counts, carry relative information about relationships between two factors. Hence, compositional tables can be seen as a generalization of (vector) compositional data. Due to their relative character, compositions are commonly expressed in orthonormal coordinates using a sequential binary partition prior to being further processed by standard statistical tools. Unfortunately, the resulting coordinates do not respect the two‐dimensional nature of compositional tables. Information about relationship between factors is thus not well captured. The aim of this paper is to present a general system of orthonormal coordinates with respect to the Aitchison geometry, which allows for an analysis of the interactions between factors in a compositional table. This is achieved using logarithms of odds ratios, which are also widely used in the context of contingency tables.
German abstract:
Compositional tables can be considered a continuous counterpart to the well‐known contingency tables. Their cells, which generally contain positive real numbers rather than just counts, carry relative information about relationships between two factors. Hence, compositional tables can be seen as a generalization of (vector) compositional data. Due to their relative character, compositions are commonly expressed in orthonormal coordinates using a sequential binary partition prior to being further processed by standard statistical tools. Unfortunately, the resulting coordinates do not respect the two‐dimensional nature of compositional tables. Information about relationship between factors is thus not well captured. The aim of this paper is to present a general system of orthonormal coordinates with respect to the Aitchison geometry, which allows for an analysis of the interactions between factors in a compositional table. This is achieved using logarithms of odds ratios, which are also widely used in the context of contingency tables.
Keywords:
Compostional Tables
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1111/sjos.12326
Electronic version of the publication:
https://onlinelibrary.wiley.com/doi/full/10.1111/sjos.12326
Created from the Publication Database of the Vienna University of Technology.