ABSTRACT
In statistical modelling, compositions can be used as predictors (independent variables, or explanatory variables) or as responses (dependent variables). As stressed throughout this book, logratio transformations of the compositions are essential, and for J-part compositions a set of J− 1 additive logratios, or a set of J− 1 independent logratios is sufficient to represent all the variance of the compositional data set. In some circumstances it may be simplifying to reduce the number of logratios by some type of variable selection process. This is always possible because logratios will always be correlated with one another, so a smaller subset of them might well be adequately “close” enough to the original set for all practical purposes.
