On stability of compositional canonical variate vector components

Abstract

AbstractCanonical variate analysis (aka discriminant coordinates) is viewed from the aspect of Aitchisonian compositional data analysis and the concept of stability in canonical vectors examined in relation to their refication (i.e. providing canonical vector components with a practical interpretation). The log-ratio transformation was found to have computational and interpretational advantages over the centred log-ratio transformation. The ad hoc application of N. A. Campbell’s application of the method of shrinkage estimators to multiple discrimination, and the optimal retention of discrimination power, is exemplified by two cases, one drawn from quantitative sedimentology, the other from biomolecular palaeontology, with the intention of probing the effect of instability on interpreting the relative importance of standardized canonical variate coefficients in relation to the suppression of near-redundant directions of within-groups variation. Pronounced instability in canonical vectors may endanger the validity of an analysis.