Publications in Scientific Journals:
P. Kynčlová, P. Filzmoser, K. Hron:
"Compositional biplots including external non-compositional variables";
STATISTICS,
50
(2016),
5;
1132
- 1148.
English abstract:
Biplots represent a widely used statistical tool for visualizing the resulting loadings and scores of a dimension reduction technique applied to multivariate data. If the underlying data carry only relative information (i.e. compositional data expressed in proportions, mg/kg, etc.) they have to be pre-processed with a logratio transformation before the dimension reduction is carried out. In the context of principal component analysis, the resulting biplot is called compositional biplot. We introduce an alternative, the ilr biplot, which is based on a special choice of orthonormal coordinates resulting from an isometric logratio (ilr) transformation. This allows to incorporate also external non-compositional variables, and to study the relations to the compositional variables. The methodology is demonstrated on real data sets.
Keywords:
compositional data, logratio transformations, principal component analysis, singularvalue decomposition, compositional biplot, ilr biplot
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1080/02331888.2015.1135155
Electronic version of the publication:
http://www.tandfonline.com/doi/full/10.1080/02331888.2015.1135155
Created from the Publication Database of the Vienna University of Technology.