Pawlowsky-Glahn V., Buccianti A. (eds.) Compositional Data Analysis: Theory and Applications

Wiley, 2011. — 390 p. — ISBN: 978-0-470-71135-4
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 scienceKey FeaturesReflects 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.A Short History of Compositional Data Analysis
Basic Concepts and Procedures
The Principle of Working on Coordinates
Dealing with Zeros
Robust Statistical Analysis
Geostatistics for Compositions
Compositional VARIMA Time Series
Compositional Data and Correspondence Analysis
Use of Survey Weights for the Analysis of Compositional Data
Notes on the Scaled Dirichlet Distribution
Elements of Simplicial Linear Algebra and Geometry
Calculus of Simplex-Valued Functions
Compositional Differential Calculus on the Simplex
Proportions, Percentages, PPM: Do the Molecular Biosciences Treat Compositional Data Right?
Hardy–Weinberg Equilibrium: A Nonparametric Compositional Approach
Compositional Analysis in Behavioural and Evolutionary Ecology
Flying in Compositional Morphospaces: Evolution of Limb Proportions in Flying Vertebrates
Natural Laws Governing the Distribution of the Elements in Geochemistry: The Role of the Log-Ratio Approach
Compositional Data Analysis in Planetology: The Surfaces of Mars and Mercury
Spectral Analysis of Compositional Data in Cyclostratigraphy
Multivariate Geochemical Data Analysis in Physical Geography
Combining Isotopic and Compositional Data: A Discrimination of Regions Prone to Nitrate Pollution
Applications in Economics
Exploratory Analysis Using CoDaPack 3D
robCompositions: An R-package for Robust Statistical Analysis of Compositional Data
Linear Models with Compositions in R