Compositional Data Analysis: Theory and Applications

Compositional Data Analysis: Theory and Applications

Editor(s): Vera Pawlowsky-Glahn, Antonella Buccianti

Published Online: 28 JUL 2011 01:44AM EST

Print ISBN: 9780470711354

Online ISBN: 9781119976462

DOI: 10.1002/9781119976462

About this Book

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.

Table of contents

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  1. Part I: Introduction

  2. Part II: Theory – Statistical Modelling

    1. Chapter 3

      The Principle of Working on Coordinates (pages 29–42)

      Glòria Mateu-Figueras, Vera Pawlowsky-Glahn and Juan José Egozcue

    2. Chapter 4

      Dealing with Zeros (pages 43–58)

      Josep Antoni Martín-Fernández, Javier Palarea-Albaladejo and Ricardo Antonio Olea

    3. Chapter 6

      Geostatistics for Compositions (pages 73–86)

      Raimon Tolosana-Delgado, Karl Gerald van den Boogaart and Vera Pawlowsky-Glahn

    4. Chapter 7

      Compositional VARIMA Time Series (pages 87–103)

      Carles Barceló-Vidal, Lucía Aguilar and Josep Antoni Martín-Fernández

    5. Chapter 10

      Notes on the Scaled Dirichlet Distribution (pages 128–138)

      Gianna Serafina Monti, Glòria Mateu-Figueras and Vera Pawlowsky-Glahn

  3. Part III: Theory – Algebra and Calculus

    1. Chapter 11

      Elements of Simplicial Linear Algebra and Geometry (pages 139–157)

      Juan José Egozcue, Carles Barceló-Vidal, Josep Antoni Martín-Fernández, Eusebi Jarauta-Bragulat, José Luis Díaz-Barrero and Glòria Mateu-Figueras

    2. Chapter 12

      Calculus of Simplex-Valued Functions (pages 158–175)

      Juan José Egozcue, Eusebi Jarauta-Bragulat and José Luis Díaz-Barrero

    3. Chapter 13

      Compositional Differential Calculus on the Simplex (pages 176–190)

      Carles Barceló-Vidal, Josep Antoni Martín-Fernández and Glòria Mateu-Figueras

  4. Part IV: Applications

    1. Chapter 17

      Flying in Compositional Morphospaces: Evolution of Limb Proportions in Flying Vertebrates (pages 235–254)

      Luis Azevedo Rodrigues, Josep Daunis-i-Estadella, Glòria Mateu-Figueras and Santiago Thió-Henestrosa

    2. Chapter 19

      Compositional Data Analysis in Planetology: The Surfaces of Mars and Mercury (pages 267–281)

      Helmut Lammer, Peter Wurz, Josep Antoni Martín-Fernández and Herbert Iwo Maria Lichtenegger

  5. Part V: Software

    1. Chapter 26

      Linear Models with Compositions in R (pages 356–371)

      Raimon Tolosana-Delgado and Karl Gerald van den Boogaart

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