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Modeling and Analysis of Compositional Data

Book Description

Modeling and Analysis of Compositional Data presents a practical and comprehensive introduction to the analysis of compositional data along with numerous examples to illustrate both theory and application of each method. Based upon short courses delivered by the authors, it provides a complete and current compendium of fundamental to advanced methodologies along with exercises at the end of each chapter to improve understanding, as well as data and a solutions manual which is available on an accompanying website.

Complementing Pawlowsky-Glahn's earlier collective text that provides an overview of the state-of-the-art in this field, Modeling and Analysis of Compositional Data fills a gap in the literature for a much-needed manual for teaching, self learning or consulting.

Table of Contents

  1. Title Page
  2. Copyright
  3. Dedication
  4. Preface
  5. About the Authors
  6. Acknowledgments
  7. Chapter 1: Introduction
  8. Chapter 2: Compositional data and their sample space
    1. 2.1 Basic concepts
    2. 2.2 Principles of compositional analysis
    3. 2.3 Zeros, missing values, and other irregular components
    4. 2.4 Exercises
  9. Chapter 3: The Aitchison geometry
    1. 3.1 General comments
    2. 3.2 Vector space structure
    3. 3.3 Inner product, norm and distance
    4. 3.4 Geometric figures
    5. 3.5 Exercises
  10. Chapter 4: Coordinate representation
    1. 4.1 Introduction
    2. 4.2 Compositional observations in real space
    3. 4.3 Generating systems
    4. 4.4 Orthonormal coordinates
    5. 4.5 Balances
    6. 4.6 Working on coordinates
    7. 4.7 Additive logratio coordinates (alr)
    8. 4.8 Orthogonal projections
    9. 4.9 Matrix operations in the simplex
    10. 4.10 Coordinates leading to alternative Euclidean structures
    11. 4.11 Exercises
  11. Chapter 5: Exploratory data analysis
    1. 5.1 General remarks
    2. 5.2 Sample center, total variance, and variation matrix
    3. 5.3 Centering and scaling
    4. 5.4 The biplot: a graphical display
    5. 5.5 Exploratory analysis of coordinates
    6. 5.6 A geological example
    7. 5.7 Linear trends along principal components
    8. 5.8 A nutrition example
    9. 5.9 A political example
    10. 5.10 Exercises
  12. Chapter 6: Random compositions
    1. 6.1 Sample space
    2. 6.2 Variability and center
    3. 6.3 Probability distributions on the simplex
    4. 6.4 Exercises
  13. Chapter 7: Statistical inference
    1. 7.1 Point estimation of center and variability
    2. 7.2 Testing hypotheses on compositional normality
    3. 7.3 Testing hypotheses about two populations
    4. 7.4 Probability and confidence regions for normal data
    5. 7.5 Bayesian estimation with count data
    6. 7.6 Exercises
  14. Chapter 8: Linear models
    1. 8.1 Linear regression with compositional response
    2. 8.2 Regression with compositional covariates
    3. 8.3 Analysis of variance with compositional response
    4. 8.4 Linear discrimination with compositional predictor
    5. 8.5 Exercises
  15. Chapter 9: Compositional processes
    1. 9.1 Linear processes
    2. 9.2 Mixture processes
    3. 9.3 Settling processes
    4. 9.4 Simplicial derivative
    5. 9.5 Elementary differential equations
    6. 9.6 Exercises
  16. Chapter 10: Epilogue
  17. References
    1. References
  18. Appendix A: Practical recipes
    1. A.1 Plotting a ternary diagram
    2. A.2 Parameterization of an elliptic region
    3. A.3 Matrix expressions of change of representation
  19. Appendix B: Random variables
    1. B.1 Probability spaces and random variables
    2. B.2 Description of probability
  20. List of abbreviations and symbols
  21. Author Index
  22. General Index
  23. Statistics in Practice
  24. End User License Agreement