This book presents the statistical analysis of compositional data using the log-ratio approach. It includes a wide range of classical and robust statistical methods adapted for compositional data analysis, such as supervised and unsupervised methods like PCA, correlation analysis, classification and regression. In addition, it considers special data structures like high-dimensional compositions and compositional tables. The methodology introduced is also frequently compared to methods which ignore the specific nature of compositional data. It focuses on practical aspects of compositional data analysis rather than on detailed theoretical derivations, thus issues like graphical visualization and preprocessing (treatment of missing values, zeros, outliers and similar artifacts) form an important part of the book. Since it is primarily intended for researchers and students from applied fields like geochemistry, chemometrics, biology and natural sciences, economics, and social sciences, all the proposed methods are accompanied by worked-out examples in R using the package robCompositions.

Fills the gap in the existing literature by providing a practical approach to compositional data analysis Presents a concise and easy-to-interpret methodology which guarantees a scale invariant analysis of data carrying relative information Uses the log-ratio approach, including various aspects of data processing Includes numerous real-world examples with implementations in R from a wide range of applications

Autorentext

Peter Filzmoser is a Professor of Statistics at the Vienna University of Technology, Austria. He received his Ph.D. and postdoctoral lecture qualification from the same university. He was a Visiting Professor at Toulouse, France and Belarus. Furthermore, he has authored more than 200 research articles and several R packages and is a co-author of a book on multivariate methods in chemometrics (CRC Press, 2009) and on analyzing environmental data (Wiley, 2008).

Karel Hron is an Associate Professor at Palacký University in Olomouc, Czech Republic. He holds a Ph.D. in applied mathematics and is active in promoting his discipline. His research activities focus on statistical analysis of compositional data and multivariate statistical analysis in general. His methods and algorithms are implemented in the statistical software R. He primarily collaborates with researchers from chemometrics and environmental sciences.

Matthias Templ is alecturer at the Zurich University of Applied Sciences, Switzerland. His main research interests include computational statistics, statistical modeling and official statistics. He is author of several R packages, such as the R package sdcMicro for statistical disclosure control, the simPop package for simulation of synthetic data, the VIM package for visualization and imputation of missing values and the package robCompositions for robust analysis of compositional data. He is author of the books Statistical Simulation in Data Science with R (Packt, 2016) and Statistical Disclosure Control (Springer, 2017).

Inhalt
Preface.- Acknowledgements.- Compositional data as a methodological concept.- Analyzing compositional data using R.- Geometrical properties of compositional data.- Exploratory data analysis and visualization.- First steps for a statistical analysis.- Cluster analysis.- Principal component analysis.- Correlation analysis.- Discriminant analysis.- Regression analysis.- Methods for high-dimensional compositional data.- Compositional tables.- Preprocessing issues.- Index.-