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Compositional biplots including external non-compositional variables
, 2013
"... 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 ..."
Abstract
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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 com-positional 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 al-lows to incorporate also external non-compositional variables, and to study the relations to the compositional variables. The methodology is demonstrated on real data sets.