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A new method for correlation analysis of compositional (environmental) data - a worked example.

C Reimann1, P Filzmoser2, K Hron3

  • 1Geological Survey of Norway, P.O.·Box 6315, 7491 Sluppen, Norway.

The Science of the Total Environment
|July 21, 2017
PubMed
Summary
This summary is machine-generated.

Environmental data are compositional, requiring specialized statistical methods. A new isometric log-ratio (ilr) transformation offers a robust approach for analyzing trace element correlations in geochemistry, avoiding misinterpretations from standard log-transformations.

Keywords:
CoDaCompositional data analysisCorrelationLog-ratio methodologyScatterplot

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Area of Science:

  • Environmental Sciences
  • Geochemistry
  • Geochemical Mapping

Background:

  • Environmental and geochemical data are often compositional, meaning variables are not independent due to fixed sums (e.g., wt%).
  • Standard statistical methods, including simple log-transformations, are often inadequate for analyzing compositional data, potentially leading to misinterpretations.
  • Bivariate and correlation analyses require appropriate log-ratio transformations to handle the relative nature of compositional variables.

Purpose of the Study:

  • To introduce and demonstrate a novel statistical approach using isometric log-ratio (ilr) transformation for analyzing compositional data in environmental sciences.
  • To highlight the limitations of traditional statistical methods (e.g., log-transformation) when applied to compositional geochemical data.
  • To illustrate the application of ilr-transformed data and heat-maps for accurate bivariate and correlation analysis using a regional soil geochemistry dataset.

Main Methods:

  • Application of the isometric log-ratio (ilr) transformation to compositional geochemical data.
  • Development and utilization of heat-maps for visualizing and summarizing correlations derived from ilr-transformed data.
  • Comparison of results from ilr-based correlation analysis with classical methods using log-transformed and raw data.

Main Results:

  • The isometric log-ratio (ilr) transformation provides symmetric coordinates suitable for compositional data analysis.
  • Heat-maps generated from ilr-transformed data offer a powerful tool for bivariate and correlation analysis.
  • Classical correlation analyses on raw or log-transformed data can lead to severe misinterpretations of element relationships in compositional datasets, even when strong correlations appear to persist.

Conclusions:

  • The isometric log-ratio (ilr) transformation is essential for accurate statistical analysis of compositional environmental and geochemical data.
  • Misconceptions regarding the independence of trace elements in compositional datasets can arise from applying inappropriate analytical methods.
  • The proposed method using ilr transformation and heat-maps enhances the reliability of geochemical data interpretation, particularly in regional mapping projects.