A robust Parafac model for compositional data

Compositional data are characterized by values containing relative information, and thus the ratios between the data values are of interest for the analysis. Due to specific features of compositional data, standard statistical methods should be applied to compositions expressed in a proper coordinate system with respect to an orthonormal basis. It is discussed how three-way compositional data can be analyzed with the Parafac model. When data are contaminated by outliers, robust estimates for the Parafac model parameters should be employed. It is demonstrated how robust estimation can be done in the context of compositional data and how the results can be interpreted. A real data example from macroeconomics underlines the usefulness of this approach.