Linear Association in Compositional Data Analysis

Authors

DOI:

https://doi.org/10.17713/ajs.v47i1.689

Abstract

With compositional data ordinary covariation indexes, designed for real random variables, fail to describe dependence. There is a need for compositional alternatives to covariance and correlation. Based on the Euclidean structure of the simplex, called Aitchison geometry, compositional association is identied to a linear restriction of the sample space when a log-contrast is constant. In order to simplify interpretation, a sparse and simple version of compositional association is dened in terms of balances which are constant across the sample. It is called b-association. This kind of association of compositional variables is extended to association between groups of compositional variables. In practice, exact b-association seldom occurs, and measures of degree of b-association are reviewed based on those previously proposed. Also, some techniques for testing b-association are studied. These techniques are applied to available oral microbiome data to illustrate both their advantages and diculties. Both testing and measurements of b-association appear to be quite sensible to heterogeneities in the studied populations and to outliers.

Author Biography

Juan José Egozcue, Universitat Politecnica de Catalunya

Dept. Civil and Environmental Engineering

Emeritus Professor

Published

2018-01-30

How to Cite

Egozcue, J. J., Pawlowsky-Glahn, V., & Gloor, G. B. (2018). Linear Association in Compositional Data Analysis. Austrian Journal of Statistics, 47(1), 3-31. https://doi.org/10.17713/ajs.v47i1.689

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Section

Articles