Robust factor analysis for compositional data

Abstract

Factor analysis as a dimension reduction technique is widely used with compositional data. Using the method for raw data or for improperly transformed data will, however, lead to biased results and consequently to misleading interpretations. Although some procedures, suitable for factor analysis with compositional data, were already developed, they require pre-knowledge of variable groups, or are complicated to handle. We present an approach based on the centred logratio (clr) transformation that does not build on this pre-knowledge, but still recognizes the specific character of compositional data. In addition, by using the isometric logratio transformation it is possible to robustify factor analysis using a robust estimation of the covariance matrix. A back-transformation of the results to the clr space allows an interpretation of the results with compositional biplots. The method is demonstrated with data from the Kola project, a large ecogeochemical mapping project in northern Europe.