Compositional Data Analysis (eBook, ePUB)
Theory and Applications
Redaktion: Pawlowsky-Glahn, Vera; Buccianti, Antonella
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Compositional Data Analysis (eBook, ePUB)
Theory and Applications
Redaktion: Pawlowsky-Glahn, Vera; Buccianti, Antonella
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It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of ``spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology,…mehr
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- Compositional Data Analysis (eBook, PDF)91,99 €
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- Bruce L. BrownMultivariate Analysis for the Biobehavioral and Social Sciences (eBook, ePUB)102,99 €
- Eric J. BehCorrespondence Analysis (eBook, ePUB)81,99 €
- Vera Pawlowsky-GlahnModeling and Analysis of Compositional Data (eBook, ePUB)72,99 €
- Daniel J. DenisUnivariate, Bivariate, and Multivariate Statistics Using R (eBook, ePUB)107,99 €
- Daniel J. DenisApplied Univariate, Bivariate, and Multivariate Statistics Using Python (eBook, ePUB)107,99 €
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- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 400
- Erscheinungstermin: 24. August 2011
- Englisch
- ISBN-13: 9781119977612
- Artikelnr.: 37345986
- Verlag: John Wiley & Sons
- Seitenzahl: 400
- Erscheinungstermin: 24. August 2011
- Englisch
- ISBN-13: 9781119977612
- Artikelnr.: 37345986
- Preface
Part One Introduction
1 A short history of compositional data analysis
1.1 Introduction
1.2 Spurious correlation
1.3 Log and log-ratio transforms
1.4 Subcompositional dependence
1.5 alr, clr, ilr: which transformation to choose?
1.6 Principles, perturbations and back to the simplex
1.7 Biplots and singular value decompositions
1.8 Mixtures
1.9 Discrete compositions
1.10 Compositional processes
1.11 Structural, counting and rounded zeros
1.12 Conclusion References
2 Basic concepts and procedures
2.1 Introduction
2.2 Election data and raw analysis
2.3 The compositional alternative
2.4 Geometric settings
2.5 Center and variability
2.6 Conclusion References Part Two Theory - Statistical Modelling
3 The principle of working on coordinates
3.1 Introduction
3.2 The role of coordinates in statistics
3.3 The simplex
3.4 Move or stay in the simplex
3.5 Conclusions References
4 Dealing with zeros
4.1 Introduction
4.2 Rounded zeros
4.3 Count zeros
4.4 Essential zeros
4.5 Difficulties, troubles and challenges References
5 Robust statistical analysis
5.1 Introduction
5.2 Elements of robust statistics from a compositional point of view
5.3 Robust methods for compositional data
5.4 Case studies
5.5 Summary References
6 Geostatistics for compositions
6.1 Introduction
6.2 A brief summary of geostatistics
6.3 Cokriging of regionalised compositions
6.4 Structural analysis of regionalised composition
6.5 Dealing with zeros: replacement strategies and simplicial indicator cokriging
6.6 Application
6.7 Conclusions References
7 Compositional VARIMA time series
7.1 Introduction
7.2 The simplex SD as a compositional space
7.3 Compositional time series models
7.4 CTS modelling: an example
7.5 Discussion
7.6 Appendix References
8 Compositional data and correspondence analysis
8.1 Introduction
8.2 Comparative technical definitions
8.3 Properties and interpretation of LRA and CA
8.4 Application to fatty acid compositional data
8.5 Discussion and conclusions References
9 Use of survey weights for the analysis of compositional data
9.1 Introduction
9.2 Elements of survey design
9.3 Application to compositional data
9.4 Discussion References
10 Notes on the scaled Dirichlet distribution
10.1 Introduction
10.2 Genesis of the scaled Dirichlet distribution
10.3 Properties of the scaled Dirichlet distribution
10.4 Conclusions References Part Three Theory - Algebra and Calculus
11 Elements of simplicial linear algebra and geometry
11.1 Introduction
11.2 Elements of simplicial geometry
11.3 Linear functions
11.4 Conclusions References
12 Calculus of simplex-valued functions
12.1 Introduction
12.2 Limits, continuity and differentiability
12.3 Integration
12.4 Conclusions References
13 Compositional differential calculus on the simplex
13.1 Introduction
13.2 Vector-valued functions on the simplex
13.3 C-derivatives on the simplex
13.4 Example: Experiments with mixtures
13.5 Discussion References Part Four Applications
14 Proportions, percentages, ppm: do the molecular biosciences treat compositional data right?
14.1 Introduction
14.2 The Omics Imp and two bioscience experiment paradigms
14.3 The impact of compositional constraints in the omics
14.4 Impact of compositional constraints on correlation and covariance
14.5 Implications References
15 Hardy-Weinberg equilibrium: a non-parametric compositional approach
15.1 Introduction
15.2 Genetic data sets
15.3 Classical tests for HWE
15.4 A compositional approach
15.5 Example
15.6 Conclusion and discussion References
16 Compositional analysis in behavioural and evolutionary ecology
16.1 Introduction
16.2 CODA in population genetics
16.3 CODA in habitat choice
16.4 Multiple choice and individual variation in preferences
16.5 Ecological specialization
16.6 Time budgets: more on specialization
16.7 Conclusions References
17 Flying in Compositional Morphospaces: evolution of limb proportions in flying vertebrates
17.1 General purpose
17.2 Flying vertebrates - general anatomical and functional characteristics
17.3 Materials
17.4 Methods
17.5 Aitchison Distances (A.D.) disparity metrics
17.6 Statistical Tests
17.7 Biplots
17.8 Balances
17.9 Size effect
17.10 Final remarks References
18 Natural laws governing the distribution of the elements in geochemistry: the role of the log-ratio approach
18.1 Introduction
18.2 Geochemical process and log-ratio approach
18.3 Log-ratio approach and water chemistry
18.4 Log-ratio approach and volcanic gas chemistry
18.5 Log-ratio approach and subducting sediment composition
18.6 Conclusions References
19 Compositional data analysis in planetology: The surfaces of Mars and Mercury
19.1 Introduction
19.2 Composition analysis of Mars' surface
19.3 Composition analysis of Mercury's surface
19.4 Conclusion References
20 Spectral Analysis of Compositional Data in Cyclostratigraphy
20.1 Introduction
20.2 The method
20.3 Case study
20.4 Discussion
20.5 Conclusions References
21 Compositional data analysis in physical geography: soil geochemistry case study
21.1 Introduction
21.2 Context
21.3 Data
21.4 Analysis
21.5 Discussion
21.6 Conclusion References
22 Combining isotopic and compositional data: a discrimination of regions prone to nitrate pollution
22.1 Introduction
22.2 Study area
22.3 Analytical methods
22.4 Statistical treatment
22.5 Results and discussion
22.6 Conclusions References
23 Applications in economics
23.1 Introduction
23.2 Consumer demand systems
23.3 Miscellaneous applications
23.4 Compositional time series
23.5 New directions
23.6 Conclusion References Part Five Software
24 Exploratory analysis using CoDaPack 3D
24.1 CoDaPack 3D description
24.2 Data set description
24.3 Exploratory analysis
24.4 Summary and conclusions References
25 robCompositions: An R-package for robust statistical analysis of compositional data
25.1 General information on the R-package robCompositions
25.2 Expressing compositional data in coordinates
25.3 Multivariate statistical methods for compositional data containing outliers
25.4 Robust imputation of missing values
25.5 Summary References
26 Linear models with compositions in R
26.1 Introduction
26.2 The illustration data set
26.3 Explanatory binary variable
26.4 Explanatory categorical variable
26.5 Explanatory continuous variable
26.6 Explanatory composition
26.7 Conclusions
- References
- Index
- Preface
Part One Introduction
1 A short history of compositional data analysis
1.1 Introduction
1.2 Spurious correlation
1.3 Log and log-ratio transforms
1.4 Subcompositional dependence
1.5 alr, clr, ilr: which transformation to choose?
1.6 Principles, perturbations and back to the simplex
1.7 Biplots and singular value decompositions
1.8 Mixtures
1.9 Discrete compositions
1.10 Compositional processes
1.11 Structural, counting and rounded zeros
1.12 Conclusion References
2 Basic concepts and procedures
2.1 Introduction
2.2 Election data and raw analysis
2.3 The compositional alternative
2.4 Geometric settings
2.5 Center and variability
2.6 Conclusion References Part Two Theory - Statistical Modelling
3 The principle of working on coordinates
3.1 Introduction
3.2 The role of coordinates in statistics
3.3 The simplex
3.4 Move or stay in the simplex
3.5 Conclusions References
4 Dealing with zeros
4.1 Introduction
4.2 Rounded zeros
4.3 Count zeros
4.4 Essential zeros
4.5 Difficulties, troubles and challenges References
5 Robust statistical analysis
5.1 Introduction
5.2 Elements of robust statistics from a compositional point of view
5.3 Robust methods for compositional data
5.4 Case studies
5.5 Summary References
6 Geostatistics for compositions
6.1 Introduction
6.2 A brief summary of geostatistics
6.3 Cokriging of regionalised compositions
6.4 Structural analysis of regionalised composition
6.5 Dealing with zeros: replacement strategies and simplicial indicator cokriging
6.6 Application
6.7 Conclusions References
7 Compositional VARIMA time series
7.1 Introduction
7.2 The simplex SD as a compositional space
7.3 Compositional time series models
7.4 CTS modelling: an example
7.5 Discussion
7.6 Appendix References
8 Compositional data and correspondence analysis
8.1 Introduction
8.2 Comparative technical definitions
8.3 Properties and interpretation of LRA and CA
8.4 Application to fatty acid compositional data
8.5 Discussion and conclusions References
9 Use of survey weights for the analysis of compositional data
9.1 Introduction
9.2 Elements of survey design
9.3 Application to compositional data
9.4 Discussion References
10 Notes on the scaled Dirichlet distribution
10.1 Introduction
10.2 Genesis of the scaled Dirichlet distribution
10.3 Properties of the scaled Dirichlet distribution
10.4 Conclusions References Part Three Theory - Algebra and Calculus
11 Elements of simplicial linear algebra and geometry
11.1 Introduction
11.2 Elements of simplicial geometry
11.3 Linear functions
11.4 Conclusions References
12 Calculus of simplex-valued functions
12.1 Introduction
12.2 Limits, continuity and differentiability
12.3 Integration
12.4 Conclusions References
13 Compositional differential calculus on the simplex
13.1 Introduction
13.2 Vector-valued functions on the simplex
13.3 C-derivatives on the simplex
13.4 Example: Experiments with mixtures
13.5 Discussion References Part Four Applications
14 Proportions, percentages, ppm: do the molecular biosciences treat compositional data right?
14.1 Introduction
14.2 The Omics Imp and two bioscience experiment paradigms
14.3 The impact of compositional constraints in the omics
14.4 Impact of compositional constraints on correlation and covariance
14.5 Implications References
15 Hardy-Weinberg equilibrium: a non-parametric compositional approach
15.1 Introduction
15.2 Genetic data sets
15.3 Classical tests for HWE
15.4 A compositional approach
15.5 Example
15.6 Conclusion and discussion References
16 Compositional analysis in behavioural and evolutionary ecology
16.1 Introduction
16.2 CODA in population genetics
16.3 CODA in habitat choice
16.4 Multiple choice and individual variation in preferences
16.5 Ecological specialization
16.6 Time budgets: more on specialization
16.7 Conclusions References
17 Flying in Compositional Morphospaces: evolution of limb proportions in flying vertebrates
17.1 General purpose
17.2 Flying vertebrates - general anatomical and functional characteristics
17.3 Materials
17.4 Methods
17.5 Aitchison Distances (A.D.) disparity metrics
17.6 Statistical Tests
17.7 Biplots
17.8 Balances
17.9 Size effect
17.10 Final remarks References
18 Natural laws governing the distribution of the elements in geochemistry: the role of the log-ratio approach
18.1 Introduction
18.2 Geochemical process and log-ratio approach
18.3 Log-ratio approach and water chemistry
18.4 Log-ratio approach and volcanic gas chemistry
18.5 Log-ratio approach and subducting sediment composition
18.6 Conclusions References
19 Compositional data analysis in planetology: The surfaces of Mars and Mercury
19.1 Introduction
19.2 Composition analysis of Mars' surface
19.3 Composition analysis of Mercury's surface
19.4 Conclusion References
20 Spectral Analysis of Compositional Data in Cyclostratigraphy
20.1 Introduction
20.2 The method
20.3 Case study
20.4 Discussion
20.5 Conclusions References
21 Compositional data analysis in physical geography: soil geochemistry case study
21.1 Introduction
21.2 Context
21.3 Data
21.4 Analysis
21.5 Discussion
21.6 Conclusion References
22 Combining isotopic and compositional data: a discrimination of regions prone to nitrate pollution
22.1 Introduction
22.2 Study area
22.3 Analytical methods
22.4 Statistical treatment
22.5 Results and discussion
22.6 Conclusions References
23 Applications in economics
23.1 Introduction
23.2 Consumer demand systems
23.3 Miscellaneous applications
23.4 Compositional time series
23.5 New directions
23.6 Conclusion References Part Five Software
24 Exploratory analysis using CoDaPack 3D
24.1 CoDaPack 3D description
24.2 Data set description
24.3 Exploratory analysis
24.4 Summary and conclusions References
25 robCompositions: An R-package for robust statistical analysis of compositional data
25.1 General information on the R-package robCompositions
25.2 Expressing compositional data in coordinates
25.3 Multivariate statistical methods for compositional data containing outliers
25.4 Robust imputation of missing values
25.5 Summary References
26 Linear models with compositions in R
26.1 Introduction
26.2 The illustration data set
26.3 Explanatory binary variable
26.4 Explanatory categorical variable
26.5 Explanatory continuous variable
26.6 Explanatory composition
26.7 Conclusions
- References
- Index