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Activity Number:
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160
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Type:
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Invited
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Date/Time:
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Tuesday, August 13, 2002 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistics & the Environment*
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| Abstract - #300538 |
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Title:
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Principles of Compositional Data Analysis
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Author(s):
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John Aitchison*+
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Affiliation(s):
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University of Glasgow
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Address:
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Rosemount, Carrick Castle, Lochgoilhead, Cairndow, Argyll, International, PA24 8AF, United Kingdom
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Keywords:
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perturbation ; powering ; ratio data ; scale invariance ; simplex ; subcompositional coherence
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Abstract:
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The statistical analysis of compositional data (vectors of proportions of some unit within a simplex sample space) has been a source of great confusion and misinterpretation in both the theoretical and applied literature. Yet the concepts and principles at the basis of such compositional problems--scale invariance, subcompositional coherence, perturbation and powering as basic operations of compositional change, some invariance requirements and a compatible simplicial metric--are simple, and lead, by a sequence of logical necessities, to two equivalent forms of statistical methodology. The first approach involves logratio transformations to real space and the use of standard unconstrained multivariate analysis. The second stay-in-the-simplex approach recognises the natural algebraic-geometric structure of the simplex as a metric vector space. Real compositional problems will be used to motivate the principles and to demonstrate practical resolutions. The relationship to ratio data analysis will be explained.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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