Compositional Data Analysis of Geological Variability and Process: A Case Study |
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| Authors: | Christopher W Thomas and John Aitchison |
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| Institution: | (1) British Geological Survey, West Main Road, Edinburgh, EH9 3LA, UK;(2) Department of Statistics, University of Glasgow, Glasgow, G12 8QQ, UK |
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| Abstract: | Developments in the statistical analysis of compositional data over the last two decades have made possible a much deeper
exploration of the nature of variability and the possible processes associated with compositional data sets from many disciplines.
In this paper, we concentrate on geochemical data. First, we explain how hypotheses of compositional variability may be formulated
within the natural sample space, the unit simplex, including useful hypotheses of sub-compositional discrimination and specific
perturbational change. Then we develop through standard methodology, such as generalised likelihood ratio tests, statistical
tools to allow the systematic investigation of a lattice of such hypotheses. Some of these tests are simple adaptations of
existing multivariate tests but others require special construction. We comment on the use of graphical methods in compositional
data analysis and on the ordination of specimens. The recent development of the concept of compositional processes is then
explained, together with the necessary tools for a staying-in-the-simplex approach, such as the singular value decomposition
of a compositional data set. All these statistical techniques are illustrated for a substantial compositional data set, consisting
of 209 major oxide and trace element compositions of metamorphosed limestones from the Grampian Highlands of Scotland. Finally,
we discuss some unresolved problems in the statistical analysis of compositional processes. |
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| Keywords: | lattice hypothesis testing logistic discriminant analysis metamorphosed limestones ordination perturbation of a composition singular value decomposition |
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