Some aspects of transformations of compositional data and the identification of outliers

The statistical analysis of compositional data is based on determining an appropriate transformation from the simplex to real space. Possible transformations and outliers strongly interact: parameters of transformations may be influenced particularly by outliers, and the result of goodness-of-fit tests will reflect their presence. Thus, the identification of outliers in compositional datasets and the selection of an appropriate transformation of the same data, are problems that cannot be separated. A robust method for outlier detection together with the likelihood of transformed data is presented as a first approach to solve those problems when the additive-logratio and multivariate Box-Cox transformations are used. Three examples illustrate the proposed methodology.