Beyond binary linear association of compositional parts

J. J. Egozcue, V. Pawlowsky-Glahn, J. A. Martín-Fernández, M. I. Ortego

In compositional data analysis, usual correlation/association coefficients (Pearson, Spearman, Kendall) are spurious. Linear association (LA) between parts, defined as proportionality of two parts along a sample, is an alternative, which can be extended to LA between groups of parts. The group or balance LA is an adequate model in genetics, e.g. for the Hardy-Weinberg equilibrium. However, detection of LAs has computational difficulties. We propose some methods to approximate general and group LAs. The best general LA is efficiently detected using the SVD of the centered clr-transformed data. However, the (almost) constant log-contrast detected in this way is frequently difficult to interpret. Approximation of the last compositional principal component (minimum variance) provides two methods to detect balance-association. Finally, exhaustive search for almost constant balances is possible using algorithms designed for principal balances, although at a high computational cost.

Palabras clave: linear association, compositional data, balance, log-contrast, linear restriction, singular value decomposition

AM-1 Análisis Multivariante
4 de septiembre de 2019  12:00
I3L8. Edificio Georgina Blanes

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