Exploring the Relationship between two Compositions using Canonical Correlation Analys
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The aim of this article is to describe a method for relating two compositions which
combines compositional data analysis and canonical correlation analysis (CCA),
and to examine its main statistical properties. We use additive log-ratio (alr)
transformation on both compositions and apply standard CCA to the transformed
data. We show that canonical variates are themselves log-ratios and log-contrasts.
The first pair of canonical variates can be interpreted as the log-contrast of a
composition that has the maximum correlation with a log-contrast of the other
composition. The second pair can be interpreted as the log-contrast of a
composition that has the maximum correlation with a log-contrast of the other
composition, under the restriction that they are uncorrelated with the first pair, and
so on.
Using properties from changes of basis, we prove that both canonical
correlations and canonical variates are invariant to the choice of divisors in alr
transformation. We show how to implement the analysis and interpret the results
by means of an illustration from the social sciences field using data from Kolb’s
Learning Style Inventory and Boyatzis’ Philosophical Orientation Questionnaire,
which distribute a fixed total score among several learning modes and
philosophical orientations
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