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Applied Compositional Data Analysis

With Worked Examples in R

  • Book
  • © 2018

Overview

Authors:
  1. Peter Filzmoser

    1. Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria

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  2. Karel Hron

    1. Department of Mathematical Analysis and Applications of Mathematics, Palacký University Olomouc, Olomouc, Czech Republic

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    You can also search for this author in PubMed   Google Scholar

  3. Matthias Templ

    1. Institute of Data Analysis and Process Design, ZHAW Zurich University of Applied Sciences, Winterthur, Switzerland

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    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Compositional Data as a Methodological Concept

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 1-16

  3. Analyzing Compositional Data Using R

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 17-34

  4. Geometrical Properties of Compositional Data

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 35-68

  5. Exploratory Data Analysis and Visualization

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 69-83

  6. First Steps for a Statistical Analysis

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 85-106

  7. Cluster Analysis

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 107-130

  8. Principal Component Analysis

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 131-148

  9. Correlation Analysis

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 149-162

  10. Discriminant Analysis

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 163-179

  11. Regression Analysis

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 181-205

  12. Methods for High-Dimensional Compositional Data

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 207-225

  13. Compositional Tables

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 227-243

  14. Preprocessing Issues

    • Peter Filzmoser, Karel Hron, Matthias Templ
    Pages 245-272

  15. Back Matter

    Pages 273-280
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Keywords

About this book

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.

Reviews

“Its great advantage is that it is very well written, easy to follow, very didactical, and self-contained. Its great advantage is that it is very well written, easy to follow, very didactical, and self-contained. … I would definitely recommend researchers to use this book, but they should be aware that compositional data analysis is not just based on simple transformations.” (Vera Pawlowsky-Glahn, Statistical Papers, Vol. 61, 2020)

“Its easy-to-read format and didactic layout are designed for researchers from different fields. … Applied Compositional Data Analysis is a nice book for scholars because it offers a wide spectrum of different types of statistical analysis.” (Jan Graffelman and Josep Antoni Martín-Fernández, Biometrical Journal, Vol. 62, 2020)

“The book is appropriate for graduate students with a basic statistical background as an introductory book to compositional data analysis using R as non-beginners. It can also be successfully used by PhD students, researchers and teachers requiring a consistent and through reference.” (Márta Ladányi, ISCB News, Vol. 68, December, 2019)

Authors and Affiliations

  • Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria

    Peter Filzmoser

  • Department of Mathematical Analysis and Applications of Mathematics, Palacký University Olomouc, Olomouc, Czech Republic

    Karel Hron

  • Institute of Data Analysis and Process Design, ZHAW Zurich University of Applied Sciences, Winterthur, Switzerland

    Matthias Templ

About the authors

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).

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