Aitchison's Compositional Data Analysis 40 Years On: A Reappraisal
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The development of John Aitchison's approach to compositional data analysis is followed since his paper read to the Royal Statistical Society in 1982. Aitchison's logratio approach, which was proposed to solve the problematic aspects of working with data with a fixed sum constraint, is summarized and reappraised. It is maintained that the principles on which this approach was originally built, the main one being subcompositional coherence, are not required to be satisfied exactly – quasi-coherence is sufficient in practice. This opens up the field to using simpler data transformations with easier interpretations and also for variable selection to be possible to make results parsimonious. The additional principle of exact isometry, which was subsequently introduced and not in Aitchison's original conception, imposed the use of isometric logratio transformations, but these have been shown to be problematic to interpret. If this principle is regarded as important, it can be relaxed by showing that simpler transformations are quasi-isometric. It is concluded that the isometric and related logratio transformations such as pivot logratios are not a prerequisite for good practice, and this conclusion is fully supported by a case study in geochemistry provided as an appendix.
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