The isometric logratio transformation in compositional data analysis: a practical evaluation

The isometric logratio transformation has been promoted by several authors as the theoretically correct way to contrast groups of parts in a compositional data set. But this transformation has only attractive theoretical properties, the practical benefits of which are questionable. A simple counter-example demonstrates the dangers of using the isometric logratio as a univariate response variable in practice. The study is then extended to a real geochemical data set, where the practical value of isometric logratios is further investigated. When groups of parts are required in practical applications, preferably based on substantive knowledge, it is demonstrated that logratios of amalgamations serve as a simpler, more intuitive and more interpretable alternative to isometric logratios. A reduced set of simple logratios of pairs of parts, possibly involving prescribed amalgamations, is adequate in accounting for the variance in a compositional data set, and highlights which parts are driving the data structure.