Aitchison’s Compositional Data Analysis 40 Years on: A Reappraisal

The development of John Aitchison’s approach to compositional data analysis is followed since his paper read the Royal Statistical Society in 1982. logratio approach, which was proposed solve problematic aspects working with a fixed-sum constraint, summarized and reappraised. It maintained that properties on this originally built, main one being subcompositional coherence, are not required be satisfied exactly—quasi-coherence sufficient, near enough coherent for all practical purposes. This opens up field using simpler transformations, such as power permit zero values data. additional property exact isometry, subsequently introduced original conception, imposed use isometric but these complicated interpret, involving ratios geometric means. If regarded important certain analytical contexts, example, unsupervised learning, it can relaxed by showing regular pairwise logratios, well alternative quasi-coherent also quasi-isometric, meaning they close isometry concluded related transformations pivot logratios prerequisite good practice, although many authors insist their obligatory use. conclusion fully supported here case studies geochemistry genomics, where performance demonstrated Aitchison, or Box–Cox transforms compositions no replacements necessary.