Compositional Data Analysis: Theory and Applications

Description

It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of ``spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. This book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. Compositional Data Analysis describes the state of the art both in theoretical fields as well as applications in the different fields of science. Key Features: Reflects the state-of-the-art in compositional data analysis. Gives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures. Looks at advances in algebra and calculus on the simplex. Presents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics. Explores connections to correspondence analysis and the Dirichlet distribution. Presents a summary of three available software packages for compositional data analysis. Supported by an accompanying website featuring R code. Applied scientists working on compositional data analysis in any field of science, both in academia and professionals will benefit from this book, along with graduate students in any field of science working with compositional data.Content: Chapter 1 A Short History of Compositional Data Analysis (pages 1–11): John Bacon?ShoneChapter 2 Basic Concepts and Procedures (pages 12–28): Juan Jose Egozcue and Vera Pawlowsky?GlahnChapter 3 The Principle of Working on Coordinates (pages 29–42): Gloria Mateu?Figueras, Vera Pawlowsky?Glahn and Juan Jose EgozcueChapter 4 Dealing with Zeros (pages 43–58): Josep Antoni Martin?Fernandez, Javier Palarea?Albaladejo and Ricardo Antonio OleaChapter 5 Robust Statistical Analysis (pages 59–72): Peter Filzmoser and Karel HronChapter 6 Geostatistics for Compositions (pages 73–86): Raimon Tolosana?Delgado, Karl Gerald van den Boogaart and Vera Pawlowsky?GlahnChapter 7 Compositional VARIMA Time Series (pages 87–103): Carles Barcelo?Vidal, Lucia Aguilar and Josep Antoni Martin?FernandezChapter 8 Compositional Data and Correspondence Analysis (pages 104–113): Michael GreenacreChapter 9 Use of Survey Weights for the Analysis of Compositional Data (pages 114–127): Monique GrafChapter 10 Notes on the Scaled Dirichlet Distribution (pages 128–138): Gianna Serafina Monti, Gloria Mateu?Figueras and Vera Pawlowsky?GlahnChapter 11 Elements of Simplicial Linear Algebra and Geometry (pages 139–157): Juan Jose Egozcue, Carles Barcelo?Vidal, Josep Antoni Martin?Fernandez, Eusebi Jarauta?Bragulat, Jose Luis Diaz?Barrero and Gloria Mateu?FiguerasChapter 12 Calculus of Simplex?Valued Functions (pages 158–175): Juan Jose Egozcue, Eusebi Jarauta?Bragulat and Jose Luis Diaz?BarreroChapter 13 Compositional Differential Calculus on the Simplex (pages 176–190): Carles Barcelo?Vidal, Josep Antoni Martin?Fernandez and Gloria Mateu?FiguerasChapter 14 Proportions, Percentages, PPM: Do the Molecular Biosciences Treat Compositional Data Right? (pages 191–207): David Lovell, Warren Muller, Jen Taylor, Alec Zwart and Chris HelliwellChapter 15 Hardy–Weinberg Equilibrium: A Nonparametric Compositional Approach (pages 208–217): Jan Graffelman and Juan Jose EgozcueChapter 16 Compositional Analysis in Behavioural and Evolutionary Ecology (pages 218–234): Michele Edoardo Raffaele Pierotti and Josep Antoni Martin?FernandezChapter 17 Flying in Compositional Morphospaces: Evolution of Limb Proportions in Flying Vertebrates (pages 235–254): Luis Azevedo Rodrigues, Josep Daunis?i?Estadella, Gloria Mateu?Figueras and Santiago Thio?HenestrosaChapter 18 Natural Laws Governing the Distribution of the Elements in Geochemistry: The Role of the Log?Ratio Approach (pages 255–266): Antonella BucciantiChapter 19 Compositional Data Analysis in Planetology: The Surfaces of Mars and Mercury (pages 267–281): Helmut Lammer, Peter Wurz, Josep Antoni Martin?Fernandez and Herbert Iwo Maria LichteneggerChapter 20 Spectral Analysis of Compositional Data in Cyclostratigraphy (pages 282–289): Eulogio Pardo?Iguzquiza and Javier HerediaChapter 21 Multivariate Geochemical Data Analysis in Physical Geography (pages 290–301): Jennifer McKinley and Christopher David LloydChapter 22 Combining Isotopic and Compositional Data: A Discrimination of Regions Prone to Nitrate Pollution (pages 302–317): Roger Puig, Raimon Tolosana?Delgado, Neus Otero and Albert FolchChapter 23 Applications in Economics (pages 318–326): Tim FryChapter 24 Exploratory Analysis Using CoDaPack 3D (pages 327–340): Santiago Thio?Henestrosa and Josep Daunis?i?EstadellaChapter 25 robCompositions: An R?package for Robust Statistical Analysis of Compositional Data (pages 341–355): Matthias Templ, Karel Hron and Peter FilzmoserChapter 26 Linear Models with Compositions in R (pages 356–371): Raimon Tolosana?Delgado and Karl Gerald van den Boogaart