Modeling and Analysis of Compositional Data

Detalles Bibliográficos
Autor principal: Pawlowsky-Glahn, Vera
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2015.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright
  • Contents
  • Preface
  • About the Authors
  • Acknowledgments
  • Chapter 1 Introduction
  • Chapter 2 Compositional Data and Their Sample Space
  • 2.1 Basic concepts
  • 2.2 Principles of compositional analysis
  • 2.2.1 Scale invariance
  • 2.2.2 Permutation invariance
  • 2.2.3 Subcompositional coherence
  • 2.3 Zeros, missing values, and other irregular components
  • 2.3.1 Kinds of irregular components
  • 2.3.2 Strategies to analyze irregular data
  • 2.4 Exercises
  • Chapter 3 The Aitchison Geometry
  • 3.1 General comments
  • 3.2 Vector space structure
  • 3.3 Inner product, norm and distance
  • 3.4 Geometric figures
  • 3.5 Exercises
  • Chapter 4 Coordinate Representation
  • 4.1 Introduction
  • 4.2 Compositional observations in real space
  • 4.3 Generating systems
  • 4.4 Orthonormal coordinates
  • 4.5 Balances
  • 4.6 Working on coordinates
  • 4.7 Additive logratio coordinates (alr)
  • 4.8 Orthogonal projections
  • 4.9 Matrix operations in the simplex
  • 4.9.1 Perturbation-linear combination of compositions
  • 4.9.2 Linear transformations of SD: endomorphisms
  • 4.9.3 Other matrix transformations on SD: nonlinear transformations
  • 4.10 Coordinates leading to alternative Euclidean structures
  • 4.11 Exercises
  • Chapter 5 Exploratory Data Analysis
  • 5.1 General remarks
  • 5.2 Sample center, total variance, and variation matrix
  • 5.3 Centering and scaling
  • 5.4 The biplot: a graphical display
  • 5.4.1 Construction of a biplot
  • 5.4.2 Interpretation of a 2D compositional biplot
  • 5.5 Exploratory analysis of coordinates
  • 5.6 A geological example
  • 5.7 Linear trends along principal components
  • 5.8 A nutrition example
  • 5.9 A political example
  • 5.10 Exercises
  • Chapter 6 Random Compositions
  • 6.1 Sample space
  • 6.1.1 Conventional approach to the sample space of compositions
  • 6.1.2 A compositional approach to the sample space of compositions
  • 6.1.3 Definitions related to random compositions
  • 6.2 Variability and center
  • 6.3 Probability distributions on the simplex
  • 6.3.1 The normal distribution on the simplex
  • 6.3.2 The Dirichlet distribution
  • 6.3.3 Other distributions
  • 6.4 Exercises
  • Chapter 7 Statistical Inference
  • 7.1 Point estimation of center and variability
  • 7.2 Testing hypotheses on compositional normality
  • 7.3 Testing hypotheses about two populations
  • 7.4 Probability and confidence regions for normal data
  • 7.5 Bayesian estimation with count data
  • 7.6 Exercises
  • Chapter 8 Linear Models
  • 8.1 Linear regression with compositional response
  • 8.2 Regression with compositional covariates
  • 8.3 Analysis of variance with compositional response
  • 8.4 Linear discrimination with compositional predictor
  • 8.5 Exercises
  • Chapter 9 Compositional Processes
  • 9.1 Linear processes
  • 9.2 Mixture processes
  • 9.3 Settling processes
  • 9.4 Simplicial derivative
  • 9.5 Elementary differential equations
  • 9.5.1 Constant derivative

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