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11 - Compositional Data

Published online by Cambridge University Press:  06 October 2017

Alan D. Chave
Affiliation:
Woods Hole Oceanographic Institution, Massachusetts
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Summary

Compositional data are multivariate data whose components sum to a constant. They are very common in the earth sciences, and are typified by the weight percent oxides in major rock analyses. Statistical tools for their analysis have only become available over the past thirty years. Compositional data are closed, and subcompositions may be obtained by applying the closure operation to a subset of a larger data set. Their sample space is the simplex, of which the simplest example is ternary. A vector space for compositional data is obtained by defining the perturbation and powering operators that are analogous to addition and multiplication in a real vector space, along with an inner product and distance measure. Transformation between the simplex and a real vector space is facilitated by centered and isometric log ratio transformations. Transformed data may be analyzed using standard tools in a real space and then transformed back to the simplex. All of these concepts are illustrated using rock composition data.
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Chapter
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Computational Statistics in the Earth Sciences
With Applications in MATLAB
, pp. 344 - 390
Publisher: Cambridge University Press
Print publication year: 2017

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  • Compositional Data
  • Alan D. Chave, Woods Hole Oceanographic Institution, Massachusetts
  • Book: Computational Statistics in the Earth Sciences
  • Online publication: 06 October 2017
  • Chapter DOI: https://doi.org/10.1017/9781316156100.012
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  • Compositional Data
  • Alan D. Chave, Woods Hole Oceanographic Institution, Massachusetts
  • Book: Computational Statistics in the Earth Sciences
  • Online publication: 06 October 2017
  • Chapter DOI: https://doi.org/10.1017/9781316156100.012
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Compositional Data
  • Alan D. Chave, Woods Hole Oceanographic Institution, Massachusetts
  • Book: Computational Statistics in the Earth Sciences
  • Online publication: 06 October 2017
  • Chapter DOI: https://doi.org/10.1017/9781316156100.012
Available formats
×