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Compositional Data Analysis Theory and Applications

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ISBN-10: 0470711353

ISBN-13: 9780470711354

Edition: 2011

Authors: Vera Pawlowsky-Glahn, Antonella Buccianti

List price: $146.00
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Description:

This book presents the state-of-the-art in compositional data analysis and will feature a collection of papers covering theory, applications to various fields of science and software. Areas covered will range from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. Key features: "#xA0;Provides the state-of-the-art text in compositional data analysis. "#xA0;Covers a variety of subject areas, from geology to medicine. "#xA0;Written by leading researchers in the field. "#xA0;Is supported by a website featuring R code.
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Book details

List price: $146.00
Copyright year: 2011
Publisher: John Wiley & Sons Canada, Limited
Publication date: 9/19/2011
Binding: Hardcover
Pages: 400
Size: 6.75" wide x 9.50" long x 0.75" tall
Weight: 0.990
Language: English

Preface
List of Contributors
Introduction
A Short History of Compositional Data Analysis
Introduction
Spurious Correlation
Log and Log-Ratio Transforms
Subcompositional Dependence
alr, clr, ilr: Which Transformation to Choose?
Principles, Perturbations and Back to the Simplex
Biplots and Singular Value Decompositions
Mixtures
Discrete Compositions
Compositional Processes
Structural, Counting and Rounded Zeros
Conclusion 9 Acknowledgement
References
Basic Concepts and Procedures
Introduction
Election Data and Raw Analysis
The Compositional Alternative
Scale Invariance: Vectors with Proportional Positive Components Represent the Same Composition
Subcompositional Coherence: Analyses Concerning a Subset of Parts Must Not Depend on Other Non-Involved Parts
Permutation Invariance: The Conclusions of a Compositional Analysis Should Not Depend on the Order of the Parts
Geometric Settings
Centre and Variability
Conclusion
Acknowledgements
References
Theory - Statistical Modelling
The Principle of Working on Coordinates
Introduction
The Role of Coordinates in Statistics
The Simplex
Basis of the Simplex
Working on Orthonormal Coordinates
Move or Stay in the Simplex
Conclusions
Acknowledgements
References
Dealing with Zeros
Introduction
Rounded Zeros
Non-Parametric Replacement of Rounded Zeros
Parametric Modified EM Algorithm for Rounded Zeros
Count Zeros
Essential Zeros
Difficulties, Troubles and Challenges
Acknowledgements
References
Robust Statistical Analysis
Introduction
Elements of Robust Statistics from a Compositional Point of View
Robust Methods for Compositional Data
Multivariate Outlier Detection
Principal Component Analysis
Discriminant Analysis
Case Studies
Multivariate Outlier Detection
Principal Component Analysis
Discriminant Analysis
Summary 70 Acknowledgement
References
Geostatistics for Compositions
Introduction
A Brief Summary of Geostatistics
Cokriging of Regionalised Compositions
Structural Analysis of Regionalised Composition
Dealing with Zeros: Replacement Strategies and Simplicial Indicator Cokriging
Application
Delimiting the Body: Simplicial Indicator Kriging
Interpolating the Oil-Brine-Solid Content
Conclusions
Acknowledgements
References
Compositional VARIMA Time Series
Introduction
The Simplex SD as a Compositional Space
Basic Concepts and Notation
The Covariance Structure on the Simplex
Compositional Time Series Models
C-Stationary Processes
C-VARIMA Processes
CTS Modelling: An Example
Expenditure Shares in the UK
Model Selection
Estimation of Parameters
Interpretation and Comparison
Discussion
Acknowledgements
References
Compositional Data and Correspondence Analysis
Introduction
Comparative Technical Definitions
Properties and Interpretation of LRA and CA
Application to Fatty Acid Compositional Data
Discussion and Conclusions
Acknowledgements
References
Use of Survey Weights for the Analysis of Compositional Data
Introduction
Elements of Survey Design
Randomization
Design-Based Estimation
Application to Compositional Data
Weighted Arithmetic and Geometric Means
Closed Arithmetic Mean of Amounts
Centred Log-Ratio of the Geometric Mean Composition
Closed Geometric Mean Composition
Example: Swiss Earnings Structure Survey (SESS)
Discussion
References
Notes on the Scaled Dirichlet Distribution
Introduction
Genesis of the Scaled Dirichlet Distribution
Properties of the Scaled Dirichlet Distribution
Graphical Comparison
Membership in the Exponential Family
Measures of Location and Variability
Conclusions
Acknowledgements
References
Theory - Algebra and Calculus
Elements of Simplicial Linear Algebra and Geometry
Introduction
Elements of Simplicial Geometry
n-Part Simplex
Vector Space
Centred Log-Ratio Representation
Metrics
Orthonormal Basis and Coordinates
Linear Functions
Linear Functions Defined on the Simplex
Simplicial Linear Function Defined on a Real Space
Simplicial Linear Function Defined on the Simplex
Conclusions
Acknowledgements
References
Calculus of Simplex-Valued Functions
Introduction
Limits, Continuity and Differentiability
Limits and Continuity
Differentiability
Higher Order Derivatives
Integration
Antiderivatives. Indefinite Integral
Integration of Continuous SV Functions
Conclusions
Acknowledgements
References
Compositional Differential Calculus on the Simplex
Introduction
Vector-Valued Functions on the Simplex
Scale-Invariant Vector-Valued Functions on Rn +
Vector-Valued Functions on Sn
C-Derivatives on the Simplex
Derivative of a Scale-Invariant Vector-Valued Function on Rn +
Directional C-Derivatives
C-Derivative
C-Gradient
Critical Points of a C-Differentiable Real-Valued Function on Sn
Example: Experiments with Mixtures
Polynomial of Degree One
Polynomial of Degree Two
Polynomial of Degree One in Logarithms
A numerical Example
Discussion
Acknowledgements
References
Applications
Proportions, Percentages, PPM: Do the Molecular Biosciences Treat Compositional Data Right?
Introduction
The Omics Imp and Two Bioscience Experiment Paradigms
The Impact of Compositional Constraints in the Omics
Univariate Impact of Compositional Constraints
Impact of Compositional Constraints on Multivariate Distance Metrics
Impact of Compositional Constraints on Correlation and Covariance
Compositional Constraints, Covariance, Correlation and Log-Transformed Data
A Simulation Approach to Understanding the Impact of Closure
Implications
Gathering Information to Infer Absolute Abundance
Analysing Compositional Omics Data Appropriately
Acknowledgements
References
Hardy-Weinberg Equilibrium: A Nonparametric Compositional Approach
Introduction
Genetic Data Sets
Classical Tests for HWE
A Compositional Approach
Example
Conclusion and Discussion
Acknowledgements
References
Compositional Analysis in Behavioural and Evolutionary Ecology
Introduction
CODA in Population Genetics
CODA in Habitat Choice
Multiple Choice and Individual Variation in Preferences
Ecological Specialization
Time Budgets: More on Specialization
Conclusions
Acknowledgements
References
Flying in Compositional Morphospaces: Evolution of Limb Proportions in Flying Vertebrates
Introduction
Flying Vertebrates - General Anatomical and Functional Characteristics
Materials
Methods
Aitchison Distance Disparity Metrics
Intragroup Aitchison Distance
Intergroup Aitchison Distance
Statistical Tests
Biplots
Chiroptera
Pterosauria
Balances
Size Effect
Final Remarks
All Groups
Aves
Pterosauria
Chiroptera
Acknowledgements
References
Natural Laws Governing the Distribution of the Elements in Geochemistry: The Role of the Log-Ratio Approach
Introduction
Geochemical Processes and Log-Ratio Approach
Log-Ratio Approach and Water Chemistry
Log-Ratio Approach and Volcanic Gas Chemistry
Log-Ratio Approach and Subducting Sediment Composition
Conclusions
Acknowledgements
References
Compositional Data Analysis in Planetology: The Surfaces of Mars and Mercury
Introduction
Mars
Mercury
Analysis of Surface Composition
Compositional Analysis of Mars' Surface
Compositional Analysis of Mercury's Surface
Conclusion 278 Acknowledgement
References
Spectral Analysis of Compositional Data in Cyclostratigraphy
Introduction
The Method
Case Study
Discussion
Conclusions 288 Acknowledgement
References
Multivariate Geochemical Data Analysis in Physical Geography
Introduction
Context
Data
Analysis
Discussion
Conclusion
Acknowledgement
References
Combining Isotopic and Compositional Data: A Discrimination of Regions Prone to Nitrate Pollution
Introduction
Study Area
Maresme
Osona
Lluc�an`es
Empord`a
Selva
Analytical Methods
Statistical Treatment
Data Scaling
Linear Discriminant Analysis
Discriminant Biplots
Results and Discussion
Conclusions
Acknowledgements
References
Applications in Economics
Introduction
Consumer Demand Systems
Miscellaneous Applications
Compositional Time Series
New Directions
Conclusion
References
Software
Exploratory Analysis Using CoDaPack 3D
CoDaPack 3D Description
Data Set Description
Exploratory Analysis
Numerical Analysis
Biplot
The Ternary Diagram
Principal Component Analysis
Balance-Dendrogram
By Groups Description
Summary and Conclusions
Acknowledgements
References
robCompositions: An R-package for Robust Statistical Analysis of Compositional Data
General Information on the R-package robCompositions
Data Sets Included in the Package
Design Principles
Expressing Compositional Data in Coordinates
Multivariate Statistical Methods for Compositional Data Containing Outliers
Multivariate Outlier Detection
Principal Component Analysis and the Robust Compositional Biplot
Discriminant Analysis
Robust Imputation of Missing Values
Summary
References
Linear Models with Compositions in R
Introduction
The Illustration Data Set
The Data
Descriptive Analysis of Compositional Characteristics
Explanatory Binary Variable
Explanatory Categorical Variable
Explanatory Continuous Variable
Explanatory Composition
Conclusions
Acknowledgement
References
Index