1. What are compositional data, and why are they special?
2. Geometry and visualization of compositional data
3. Logratio transformations
4. Properties and distributions of logratios
5. Clustering of compositional data
6. Dimension reduction using logratio analysis
7. Regression models involving compositional data
8. The zeros problem, with some solutions
9. Variable selection for unsupervised and supervised learning
10. To weight or not to weight
11. The analysis of complete compositions
12. The analysis of shape
13. High-dimensional “omics” data
14. Case study 1: Fatty acid compositions of marine amphipods
15. Case study 2: Sedimentological modelling with compositional predictors
16. Case study 3: Ecological modeling with compositional responses
Biography
Michael Greenacre is “Professor Talent Superior” in the Department of Economics and Business of the Universitat Pompeu Fabra, Barcelona, where he has worked for 31 years until his recent retirement. He has written over 100 research articles, as well as eight books, including three editions of Correspondence Analysis in Practice (1993, 2007, 2016), which has been translated into Spanish and Japanese. He has also edited four books with Jörg Blasius of Bonn University, on correspondence analysis and related methods. He continues to work and publish actively in correspondence analysis and compositional data analysis, in collaboration with researchers in several countries, in the fields of biochemistry, geochemistry, archaeology, genomics and ecology, with a recent new interest in sensometrics (statistics of sensory data). He is also a musician and composer, and has published two albums of his own compositions, “You, Woman” and “Below the Surface”, with the singer Gurdeep Stephens and guitarist Santi Careta, and has a popular YouTube channel of his satirical statistical songs.
“Michael Greenacre is a world expert on CoDA, having taking the mantle from his mentor and friend John Aitchison. After introducing the logratio transforms early in the book, they are used in a wide and interesting set of applications in subsequent chapters. By sticking to a strict eight-page limit per chapter, Greenacre is forced to write with clarity but sufficient detail to get the concepts across, always ending in a concise half page summary. A welcome appendix gives some additional details for those like me who “need to know”. This book would make for a wonderful one semester course in applied multivariate statistics, suitable for upper level undergraduates or masters students in data science.”
~Trevor Hastie, The John A. Overdeck Professor, Professor of Statistics and Biomedical Data Science (emeritus), Stanford University, USA“This book is a small gem that will find its place among those who are interested in learning about this important topic from a master of clarity and exposition. It fills a real need: a principled, practical introduction built around logratios, which guarantee the subcompositional coherence that treating proportions as ordinary measurements cannot. Thirteen methodological chapters progress from fundamentals – what makes compositional data special, simplex geometry, logratio transformations – through clustering, dimension reduction, regression, variable selection, the zeros problem, and the surprising finding that for high-dimensional omics data, logratio transformation may not be necessary at all. Three integrative case studies from marine biology, sedimentology, and ecology then demonstrate the full workflow in practice. Key features include diverse real-data examples throughout, concise chapter-end summaries, a mathematical appendix, and a companion R package, ‘easyCODA’, released alongside the book. Graduate students and applied researchers across the quantitative sciences who encounter proportional data will find this an authoritative yet accessible guide.”
~Michael Friendly, York University, Canada“This book is an excellent introduction to Compositional Data Analysis (CoDA). Aitchison’s main principles, permutation and scale invariance, subcompositional coherence, as well as simplex geometry, spurious correlations and ternary diagrams are well-explained. The mainstay of CoDA, the logratio transformations, are well-motivated and integrated into many multivariate methods, such as (constrained) principal component analysis, generalised linear models, cluster analysis, classification and regression trees and others. Theoretical statistical background, bibliography and computational details are provided in three appendices. The book has a very strong data-analytic focus, using data to motivate the conceptual development and illustrate methods; three chapters consist of data-analytic case studies. The computational appendix, based on the author’s R-package easyCODA,enables the reader to reproduce examples and analyse compositional data. The text covers many interesting applications ranging from geology to ecology, biochemistry, genomics and other fields. Distinctive features are the innovative use of weights in the compositional context, the extensive use of biplots to achieve dimension reduction and attractive visualisations, and particular choices of the author to deal with zeros and select convenient logratio transformations. The book is an inspiring text for applied scientists and graduate students with background in multivariate analysis and interested in mastering the analysis of compositional data.”
~Jan Graffelman, Professor, Technical University of Catalonia“This new edition offers new insights in how to view and analyze compositional data. The section on Logratio Transformation has been completely re-written and provides a comprehensive and systematic review of the various logratio transformations that can be used. The chapters on Clustering of compositional data and Dimension reduction using logratio analysis offer new insights with examples including geochemical analysis and fish morphology. It also includes four new chapters: To weight or not to weight; The analysis of complete compositions; The analysis of shape and High-dimensional “omics” data. There are now three case studies; along with Appendices that include: the theory of compositional data analysis; an extended bibliography, including web resources; sources for datasets used in the book; a guide to the easyCODA software for compositional data analysis; a glossary of terms; and an Epilogue. Overall, this expanded edition offers an enhanced way of evaluating compositional data and reflects the recent developments in how compositional data are analyzed. As with the first edition, the second edition can be used at the undergraduate level as part of a course in data analysis. At the graduate level, for research studies, this book provides a comprehensive approach, providing insight for effective interpretation for a wide range of compositional data types.”
~ Eric Grunsky, Department of Earth and Environmental Sciences, University of Waterloo, Canada“Compositional data show the proportions of the different parts or components of some whole and arise in many sciences, such as biology, geology or economics. Chemical composition of rock samples is just one example among many. The constraint that relative amounts or counts have a constant sum both simplifies and complicates their analysis. Modern approaches have grown from the insistence of John Aitchison that ratios for different parts are key and best analysed on logarithmic scale. Yet problems remain, notably the frequent occurrence of zeros. The ballooning recent literature has ranged from numerous applications to elaborate mathematical developments. Michael Greenacre's book in 2019 provided a concise but thorough and innovative guide to the most important ideas, connecting with complementary methods such as correspondence analysis. Expositions and examples were linked to general ideas on visualization, multivariate analysis, and modelling. Michael's second edition is now richer, with six new chapters and updating of material. This is where people with some grounding in statistics but new to the topic should start for a fresh but original overview.”
~Nicholas J. Cox, Durham University, UK
