Resumen de A practical evaluation of the isometric logratio transformation
Michael Greenacre, Eric C. Grunsky, John Bacon-Shone
The isometric logratio (ILR) transformation, which is a logratio of geometric means, has been promoted by several authors as the required way, from a theoretical viewpoint, to contrast groups of compositional parts and form a set of new coordinates for analysing a compositional data set. The interpretation of ILRs is made complicated by the fact that each geometric mean depends on the relative values of all the parts included in it. Thus, the geometric mean should never be interpreted as an amalgamation of parts, except in some very special cases that hardly ever occur in practice. Simple examples can be constructed to show the dangers in using ILRs in statistical modelling. In fact, ILRs should never be used as univariate statistics because of their unclear interpretation. Furthermore, the mathematical properties of the ILR transformation, which justify its existence, are found to be not required for good practice in compositional data analysis. 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 ILRs. 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. The necessity to address the research question is also stressed, as opposed to the conversion of the data to ILR coordinates in an automatic way.
