General approach to coordinate representation of compositional tables
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2018
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01A - Journal article
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Scandinavian Journal of Statistics
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45
Issue / Number
4
Pages / Duration
879-899
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Wiley
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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.
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0303-6898
Language
English
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No
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Published
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Citation
Facevicova, K., Hron, K., Todorov, V., & Templ, M. (2018). General approach to coordinate representation of compositional tables. Scandinavian Journal of Statistics, 45(4), 879–899. https://doi.org/10.1111/sjos.12326