Compositional Data Analysis in the Geosciences: from Theory to Practice

A composition is a variate with elements that are constrained to sum to a constant. Compositions are common in the geosciences. A rock may be characterized by the proportions of different minerals or elements whereas a soil or sediment is described by the percentages of the mineral particles in different size classes. The analysis of compositions must allow for the constrained sample space from which they are drawn. This book is a collection of articles on the analysis of compositions in geosciences by some well-known practitioners. Vera Pawlowsky-Glahn and Juan Jose Ecozgue introduce it with a concise account of compositions and their properties, log-ratio transforms and some basic issues of data presentation and manipulation. The rest of the book comprises three sections. The first of these presents case-studies from the geosciences. In a typical problem the geoscientist wants to extract information from a mineralogical or elemental analysis of material. For example, Thomas and Aitchison show how a logistic regression on the elements of a composition can be used to discriminate between limestone samples from different formations. A model selection procedure was used to find the subcomposition that was most effective for discrimination. Having established the model with material from sites where the stratigraphy is well understood, the authors applied it to elucidate the stratigraphy elsewhere where field mapping had been less successful because of poorer exposure. The second part comprises three papers on software: one stand-alone program and two packages for R. These seem well presented, nicely illustrated and thorough for the reader who wants to start to do compositional analysis. The final section returns to theoretical and methodological questions. There is a useful chapter on exploratory data analysis, another on the vexing question of zero values in compositions and a revisiting of the question of whether we can postulate general rules for the distribution of geochemical variables. This book will be valuable for geoscientists and the statisticians who advise them. Each chapter is presented as a stand-alone paper, which leads to some repetition, but there is an index which has been produced with care. I was disappointed by the curious silence on compositional geostatistics. The literature on this topic includes a book by one of the editors (Pawlowsky-Glahn and Olea, 2004), so it seems strange that the problem of characterizing the spatial correlation of compositional variates and predicting them at unsampled sites has not been tackled in this otherwise thorough treatment of an important area.