Vera Pawlowsky-Glahn, Juan José Egozcue, Raimon Tolosana-Delgado

Modeling and Analysis of Compositional Data (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 272
• Erscheinungstermin: 17. Februar 2015
• Englisch
• ISBN-13: 9781119003113
• Artikelnr.: 42366337

Autorenporträt

VERA PAWLOWSKY-GLAHN Department of Computer Science, Applied Mathematics, and Statistics, University of Girona, Spain JUAN JOSÉ EGOZCUE Department of Applied Mathematics III, Technical University of Catalonia, Barcelona, Spain RAIMON TOLOSANA-DELGADO Helmholtz Institute Freiberg for Resource Technology, Germany

Inhaltsangabe

Preface xi About the Authors xv Acknowledgments xix 1 Introduction 1 2
Compositional Data and Their Sample Space 8 2.1 Basic concepts 8 2.2
Principles of compositional analysis 12 2.2.1 Scale invariance 12 2.2.2
Permutation invariance 15 2.2.3 Subcompositional coherence 16 2.3 Zeros,
missing values, and other irregular components 16 2.3.1 Kinds of irregular
components 16 2.3.2 Strategies to analyze irregular data 19 2.4 Exercises
21 3 The Aitchison Geometry 23 3.1 General comments 23 3.2 Vector space
structure 24 3.3 Inner product, norm and distance 26 3.4 Geometric figures
28 3.5 Exercises 30 4 Coordinate Representation 32 4.1 Introduction 32 4.2
Compositional observations in real space 33 4.3 Generating systems 33 4.4
Orthonormal coordinates 36 4.5 Balances 38 4.6 Working on coordinates 43
4.7 Additive logratio coordinates (alr) 46 4.8 Orthogonal projections 48
4.9 Matrix operations in the simplex 54 4.9.1 Perturbation-linear
combination of compositions 54 4.9.2 Linear transformations of óKòù:
endomorphisms 55 4.9.3 Other matrix transformations on óKòù: nonlinear
transformations 57 4.10 Coordinates leading to alternative Euclidean
structures 59 4.11 Exercises 61 5 Exploratory Data Analysis 65 5.1 General
remarks 65 5.2 Sample center, total variance, and variation matrix 66 5.3
Centering and scaling 68 5.4 The biplot: a graphical display 70 5.4.1
Construction of a biplot 70 5.4.2 Interpretation of a 2D compositional
biplot 72 5.5 Exploratory analysis of coordinates 76 5.6 A geological
example 79 5.7 Linear trends along principal components 85 5.8 A nutrition
example 89 5.9 A political example 96 5.10 Exercises 100 6 Random
Compositions 103 6.1 Sample space 103 6.1.1 Conventional approach to the
sample space of compositions 105 6.1.2 A compositional approach to the
sample space of compositions 106 6.1.3 Definitions related to random
compositions 107 6.2 Variability and center 108 6.3 Probability
distributions on the simplex 112 6.3.1 The normal distribution on the
simplex 114 6.3.2 The Dirichlet distribution 121 6.3.3 Other distributions
127 6.4 Exercises 128 7 Statistical Inference 130 7.1 Point estimation of
center and variability 130 7.2 Testing hypotheses on compositional
normality 135 7.3 Testing hypotheses about two populations 136 7.4
Probability and confidence regions for normal data 142 7.5 Bayesian
estimation with count data 144 7.6 Exercises 147 8 Linear Models 149 8.1
Linear regression with compositional response 150 8.2 Regression with
compositional covariates 156 8.3 Analysis of variance with compositional
response 160 8.4 Linear discrimination with compositional predictor 163 8.5
Exercises 165 9 Compositional Processes 172 9.1 Linear processes 173 9.2
Mixture processes 176 9.3 Settling processes 178 9.4 Simplicial derivative
183 9.5 Elementary differential equations 186 9.5.1 Constant derivative 187
9.5.2 Forced derivative 189 9.5.3 Complete first-order linear equation 194
9.5.4 Harmonic oscillator 200 9.6 Exercises 204 10 Epilogue 206 References
211 Appendix A Practical Recipes 222 A.1 Plotting a ternary diagram 222 A.2
Parameterization of an elliptic region 224 A.3 Matrix expressions of change
of representation 226 Appendix B Random Variables 228 B.1 Probability
spaces and random variables 228 B.2 Description of probability 232 List of
Abbreviations and Symbols 234 Author Index 237 General Index 241