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The approach to analysing compositional data has been dominated by the use oflogratio transformations, to ensure exact subcompositional coherence and, insome situations, exact isometry as well. A problem with this approach is thatdata zeros, found in most applications, have to be replaced to allow thelogarithmic transformation. An alternative new approach, called the `chiPower'transformation, which allows data zeros, is to combine the standardizationinherent in the chi-square distance in correspondence analysis, with theessential elements of the Box-Cox power transformation. The chiPowertransformation is justified because it} defines between-sample distances thattend to logratio distances for strictly positive data as the power parametertends to zero, and are then equivalent to transforming to logratios. For datawith zeros, a value of the power can be identified that brings the chiPowertransformation as close as possible to a logratio transformation, withouthaving to substitute the zeros. Especially in the area of high-dimensionaldata, this alternative approach can present such a high level of coherence andisometry as to be a valid approach to the analysis of compositional data.Furthermore, in a supervised learning context, if the compositional variablesserve as predictors of a response in a modelling framework, for examplegeneralized linear models, then the power can be used as a tuning parameter inoptimizing the accuracy of prediction through cross-validation. ThechiPower-transformed variables have a straightforward interpretation, sincethey are each identified with single compositional parts, not ratios.

The chiPower transformation: a valid alternative to logratio transformations in compositional data analysis