Dealing with Zeros and Missing Values in Compositional Data Sets Using Nonparametric Imputation

The statistical analysis of compositional data based on logratios of parts is not suitable when zeros are present in a data set. Nevertheless, if there is interest in using this modeling approach, several strategies have been published in the specialized literature which can be used. In particular, substitution or imputation strategies are available for rounded zeros. In this paper, existing nonparametric imputation methods—both for the additive and the multiplicative approach—are revised and essential properties of the last method are given. For missing values a generalization of the multiplicative approach is proposed.     

The logratio approach to the classification of modern sediments and sedimentary environments in northern South China Sea

Grain-size measurements are a type of compositional data and thus subject to closure effects and nonnormality. The logratio transform of Aitchison successfully resolves these problems in compositional data analysis. An application to modern sediment data from the northern part of the South China Sea demonstrates that logratio principal components analysis provides a clear separation of data which cannot be obtained by ordinary principal components analysis, and that cluster analysis using logratio principal components gives a much better classification of sediments than does cluster analysis using raw data. The delineation of sedimentary environments on the basis of a logratio classification of sediment samples provides a better understanding of hydrodynamic conditions on the shelf.