Modeling and Analysis of Compositional Data

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