Compositional biplots including external non-compositional variables

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 p...

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Bibliographic Details
Published inStatistics (Berlin, DDR) Vol. 50; no. 5; pp. 1132 - 1148
Main Authors Kynčlová, P., Filzmoser, P., Hron, K.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.09.2016
Taylor & Francis Ltd
Subjects
compositional biplot
compositional data
ilr biplot
logratio transformations
Multivariate analysis
principal component analysis
Principal components analysis
Reduction
Regression analysis
singularvalue decomposition
Transformations
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Summary: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.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331888.2015.1135155