Modeling and Analysis of Compositional Data

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Statistical analysis of compositional data has been a topic of research for more than a century, within the last decade, theoretical results have shown that the simplex--the sample space of compositional data--can be structured as a Euclidean space. This allows the representation of compositions in coordinates, in particular, in coordinates with respect to an orthonormal (Cartesian) basis. In turn, it offers a way to apply all known methods in multivariate statistics, which were developed under the assumption that data are realizations of real random variables. Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction with numerous examples to illustrate both theory and application of each method. The authors provide a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to aid the readers' understanding. Solutions to questions raised throughout the text, along with datasets, are available on the companion website (www.wiley.com/go/glahn/practical). * Presents a comprehensive and practical introduction to the analysis of compositional data. * Presents numerous examples of compositional data and exercises from many fields of science. * Uses a sample space approach to compositional data based on its algebraic/geometric structure. * Written by leading experts responsible for many advances in the field. * Accompanied by a website featuring a manual with solutions, instructions to access free software, and datasets. Statisticians, mathematicians, and researchers in all fields of science that have to deal with compositional data will find this book a useful resource. It can also be used as a textbook for students with basic knowledge of linear algebra, calculus, and statistics.