Interpretation of orthonormal coordinates in case of three-part compositions applied to orthogonal regression for compositional data.
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Inclou dades d'ús des de 2022
Cita com:
hdl:2117/366680
Tipus de documentText en actes de congrés
Data publicació2011
EditorCIMNE
Condicions d'accésAccés obert
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Abstract
Orthonormal coordinates are very important tool for compositional data processing using standard
statistical methods. Namely, in order to express a D-part composition in the Euclidean real space we
use isometric log-ratio (ilr) transformation, which is an isometric mapping from the sample space of
compositions, the simplex S
D with the Aitchison geometry, to the (D −1)-dimensional Euclidean real
space RD−1
. The ilr transformation results in coordinates of an orthonormal basis on the simplex.
Advantages coming from this transformation, like the mentioned isometry between S
D and RD−1
, are
closely related with the problem of interpreting orthonormal coordinates, constructed by sequential
binary partition. Their interpretation can be approached as balances between groups of parts of a
composition as well as by expressing their covariance structure by log-ratios of parts of the analyzed
composition, i.e. in terms of ratios. Note that if we want to achieve interpretation of results of
statistical analysis directly on the simplex (in terms of the original compositional parts), the backtransformation is required.
CitacióDonevska, S.; Fiserová, E.; Hron, K. Interpretation of orthonormal coordinates in case of three-part compositions applied to orthogonal regression for compositional data. A: CODAWORK 2011. "Proceedings of CoDaWork'11: 4th international workshop on Compositional Data Analysis, Egozcue, J.J., Tolosana-Delgado, R. and Ortego, M.I. (eds.) 2011". Barcelona: CIMNE, 2011, ISBN 978-84-87867-76-7.
ISBN978-84-87867-76-7
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