Compositional data analysis: theory and applications
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| Format: | Book |
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| Language: | English |
| Published: |
Hoboken, N.J.
Wiley
2011
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXI, 378 S. Ill., graph. Darst., Kt. |
| ISBN: | 9780470711354 |
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MARC
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| 245 | 1 | 0 | |a Compositional data analysis |b theory and applications |c ed. by Vera Pawlowsky-Glahn ... |
| 264 | 1 | |a Hoboken, N.J. |b Wiley |c 2011 | |
| 300 | |a XXI, 378 S. |b Ill., graph. Darst., Kt. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Correlation (Statistics) | |
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| 700 | 1 | |a Pawlowsky-Glahn, Vera |e Sonstige |4 oth | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
xvii
List of Contributors
xix
Part I Introduction
1
1
A Short History of Compositional Data Analysis
3
John Bacon-Shone
1.1
Introduction
3
1.2
Spurious Correlation
3
1.3
Log and Log-Ratio Transforms
4
1.4
Subcompositionai Dependence
5
1.5
air, clr, ilr: Which Transformation to Choose?
5
1.6
Principles, Perturbations and Back to the Simplex
6
1.7
Biplots and Singular Value Decompositions
7
1.8
Mixtures
7
1.9
Discrete Compositions
8
1.10
Compositional Processes
8
1.11
Structural, Counting and Rounded Zeros
8
1.12
Conclusion
9
Acknowledgement
9
References
9
2
Basic Concepts and Procedures
12
Juan
José Egozcue
and
Vera Pawlowsky-Glahn
2.1
Introduction
12
2.2
Election Data and Raw Analysis
13
2.3
The Compositional Alternative
15
2.3.1
Scale
Invariance:
Vectors with Proportional Positive Components
Represent the Same Composition
15
2.3.2
Subcompositionai Coherence: Analyses Concerning a Subset of
Parts Must Not Depend on Other Non-Involved Parts
16
viii CONTENTS
2.3.3
Permutation Invariance: The Conclusions
of a Compositional
Analysis Should Not Depend on the Order of the Parts
17
2.4
Geometric Settings
17
2.5
Centre and Variability
22
2.6
Conclusion
27
Acknowledgements
27
References
27
Part II Theory
-
Statistical Modelling
29
3
The Principle of Working on Coordinates
31
Gloria
Mateu-Figueras, Vera
Pawlowsky-Glahn and Juan
José Egozcue
3.1
Introduction
31
3.2
The Role of Coordinates in Statistics
32
3.3
The Simplex
33
3.3.1
Basis of the Simplex
34
3.3.2
Working on
Orthonormal
Coordinates
35
3.4
Move or Stay in the Simplex
38
3.5
Conclusions
40
Acknowledgements
41
References
41
4
Dealing with Zeros
43
Josep
Antoni
Martín-Fernández,
Javier Palarea-Albaladejo and
Ricardo
Antonio
Olea
4.1
Introduction
43
4.2
Rounded Zeros
44
4.2.1
Non-Parametric Replacement of Rounded Zeros
45
4.2.2
Parametric Modified EM Algorithm for Rounded Zeros
47
4.3
Count Zeros
50
4.4
Essential Zeros
53
4.5
Difficulties, Troubles and Challenges
55
Acknowledgements
57
References
57
5
Robust Statistical Analysis
59
Peter
Filzmoser
and
Karel Hron
5.1
Introduction
59
5.2
Elements of Robust Statistics from a Compositional Point of View
60
5.3
Robust Methods for Compositional Data
63
5.3.1
Multivariate Outlier Detection
64
5.3.2
Principal Component Analysis
64
5.3.3
Discriminant Analysis
65
5.4
Case Studies
66
5.4.1
Multivariate Outlier Detection
66
5.4.2
Principal Component Analysis
68
5.4.3
Discriminant Analysis
68
5.5
Summary
70
CONTENTS ix
Acknowledgement
71
References
71
6
Geostatistics for Compositions
73
Raimon Tolosana-Delgado, Karl Gerald van den Boogaart and
Vera Pawlowsky-Glahn
6.1
Introduction
73
6.2
A Brief Summary of Geostatistics
74
6.3
Cokriging of
Regionalised
Compositions
76
6.4
Structural Analysis of
Regionalised
Composition
76
6.5
Dealing with Zeros: Replacement Strategies and Simplicial
Indicator Cokriging
78
6.6
Application
79
6.6.1
Delimiting the Body: Simplicial Indicator Kriging
81
6.6.2
Interpolating the Oil-Brine-Solid Content
82
6.7
Conclusions
84
Acknowledgements
84
References
84
7
Compositional VARIMA Time Series
87
Carles
Barceló-Vidal
,
Lucía
Aguilar andJosep
Antoni
Martín-Fernández
7.1
Introduction
87
7.2
The Simplex SD as a Compositional Space
89
7.2.1
Basic Concepts and Notation
89
7.2.2
The Covariance Structure on the Simplex
90
7.3
Compositional Time Series Models
91
7.3.1
С
-Stationary Processes
92
7.3.2
¿ľ-
VARIMA Processes
93
7.4
CTS Modelling: An Example
94
7.4.1
Expenditure Shares in the UK
94
7.4.2
Model Selection
95
7.4.3
Estimation of Parameters
96
7.4.4
Interpretation and Comparison
96
7.5
Discussion
99
Acknowledgements
99
References
100
Appendix
102
8
Compositional Data and Correspondence Analysis
104
Michael
Greenacre
8.1
Introduction
104
8.2
Comparative Technical Definitions
105
8.3
Properties and Interpretation of LRA and
С А
107
8.4
Application to Fatty Acid Compositional Data
107
8.5
Discussion and Conclusions
111
Acknowledgements
112
References
112
χ
CONTENTS
9
Use of Survey Weights for the Analysis of Compositional Data
114
Monique
Graf
9.1
Introduction
114
9.2
Elements of Survey Design
115
9.2.1
Randomization
115
9.2.2
Design-Based Estimation
118
9.3
Application to Compositional Data
122
9.3.1
Weighted Arithmetic and Geometric Means
123
9.3.2
Closed Arithmetic Mean of Amounts
123
9.3.3
Centred Log-Ratio of the Geometric Mean Composition
124
9.3.4
Closed Geometric Mean Composition
124
9.3.5
Example: Swiss Earnings Structure Survey (SESS)
125
9.4
Discussion
126
References
126
10
Notes on the Scaled Dirichlet Distribution
128
Gianna
Serafina
Monti, Gloria Mateu-Figueras and
Vera Pawlowsky-Glahn
10.1
Introduction
128
10.2
Genesis of the Scaled Dirichlet Distribution
129
10.3
Properties of the Scaled Dirichlet Distribution
131
10.3.1
Graphical Comparison
131
10.3.2
Membership in the Exponential Family
133
10.3.3
Measures of Location and Variability
134
10.4
Conclusions
136
Acknowledgements
137
References
137
Part III Theory
-
Algebra and Calculus
139
11
Elements of Simplicial Linear Algebra and Geometry
141
Juan José
Egozcue, Carles
Barceló-Vidal,
Josep
Antoni
Martín-Fernández,
Eusebi Jarauta-Bragulat,
José Luis Díaz-Barrero
and Gloria Mateu-Figueras
11.1
Introduction
141
11.2
Elements of Simplicial Geometry
142
11.2.1
η
-Part
Simplex
142
11.2.2
Vector Space
143
11.2.3
Centred Log-Ratio Representation
146
11.2.4
Metrics
147
11.2.5
Orthonormal
Basis and Coordinates
149
11.3
Linear Functions
151
11.3.1
Linear Functions Defined on the Simplex
152
11.3.2
Simplicial Linear Function Defined on a Real Space
153
11.3.3
Simplicial Linear Function Defined on the Simplex
154
11.4
Conclusions
156
Acknowledgements
156
References
156
CONTENTS xi
12
Calculus of
Simplex-
Valued Functions
158
Juan
José Egozcue,
Eusebi Jarauta-Bragulat and
José Luis Díaz-Barrero
12.1
Introduction
158
12.2
Limits, Continuity and Differentiability
161
12.2.1
Limits and Continuity
161
12.2.2
Differentiability
163
12.2.3
Higher Order Derivatives
169
12.3
Integration
171
12.3.1 Antiderivatives.
Indefinite Integral
171
12.3.2
Integration of Continuous SV Functions
172
12.4
Conclusions
174
Acknowledgements
175
References
175
13
Compositional Differential Calculus on the Simplex
176
Carles
Barceló-Vidal,
Josep
Antoni
Martín-Fernández
and Gloria Mateu-Figueras
13.1
Introduction
176
13.2
Vector-Valued Functions on the Simplex
177
13.2.1
Scale-Invariant Vector-Valued Functions on
Ш +
177
13.2.2
Vector-Valued Functions on <S
178
13.3
C-Derivatives on the Simplex
178
13.3.1
Derivative of a Scale-Invariant Vector-Valued Function on R+
178
13.3.2
Directional C-Derivatives
180
13.3.3
C-Derivative
182
13.3.4
C-Gradient
184
13.3.5
Critical Points of a C-Differentiable Real-Valued Function
on S
184
13.4
Example: Experiments with Mixtures
185
13.4.1
Polynomial of Degree One
185
13.4.2
Polynomial of Degree Two
186
13.4.3
Polynomial of Degree One in Logarithms
187
13.4.4
A numerical Example
188
13.5
Discussion
189
Acknowledgements
190
References
190
Part IV Applications
191
14
Proportions, Percentages, PPM: Do the Molecular
Biosciences
Treat Compositional Data Right?
193
David Lovell, Warren
Müller, Jen
Taylor, Alec
Zwart
and Chris Helliwell
14.1
Introduction
193
14.2
The Omics Imp and Two
Bioscience
Experiment Paradigms
194
14.3
The Impact of Compositional Constraints in the Omics
197
14.3.1
Univariate Impact of Compositional Constraints
197
14.3.2
Impact of Compositional Constraints on Multivariate
Distance Metrics
199
15
CONTENTS
14.4
Impact
of Compositional Constraints on Correlation and Covariance
201
14.4.1
Compositional Constraints, Covariance, Correlation
and Log-Transformed Data
202
14.4.2
A Simulation Approach to Understanding the Impact of
Closure
202
14.5
Implications
204
14.5.1
Gathering Information to Infer Absolute Abundance
204
14.5.2
Analysing Compositional Omics Data Appropriately
205
Acknowledgements
206
References
206
Hardy-
Weinberg
Equilibrium: A Nonparametric Compositional Approach
208
Jan Graffelman and Juan
José Egozcue
15.1
Introduction
208
15.2
Genetic Data Sets
209
15.3
Classical Tests for HWE
210
15.4
A Compositional Approach
210
15.5
Example
214
15.6
Conclusion and Discussion
215
Acknowledgements
215
References
215
16
Compositional Analysis in Behavioural and Evolutionary Ecology
218
Michele Edoardo Raffaele
Ρ
¡erotti
andJosep
Antoni
Martín-Fernández
16.1
Introduction
218
16.2
CODA in
Population Genetics
219
16.3
CODA in Habitat
Choice
222
16.4
Multiple
Choice and Individual Variation in Preferences
224
16.5
Ecological Specialization
228
16.6
Time Budgets: More on Specialization
229
16.7
Conclusions
231
Acknowledgements
231
References
231
17
Flying in Compositional Morphospaces: Evolution of Limb Proportions
in Flying Vertebrates
235
Luis
Azevedo
Rodrigues,
Josep Daunis-i-Estadella, Gloria Mateu-Figueras
and Santiago
Thió-H
ene strosa
17.1
Introduction
235
17.2
Flying Vertebrates
-
General Anatomical and Functional Characteristics
236
17.3
Materials
236
17.4
Methods
238
17.5
Aitchison Distance Disparity Metrics
239
17.5.1
Intragroup Aitchison Distance
239
17.5.2
Intergroup Aitchison Distance
240
17.6
Statistical Tests
243
17.7 Biplots
17.7.1
Chiroptera
17.7.2
Pterosauria
17.8
Balances
17.9
Size Effect
17.10
Final Remarks
17.10.1
All Groups
17.10.2
Aves
17.10.3
Pterosauria
17.10.4
Chiroptera
Acknowledgements
References
CONTENTS
xiii
244
244
245
246
249
249
250
250
250
251
252
252
18
Natural Laws Governing the Distribution of the Elements
in Geochemistry: The Role of the Log-Ratio Approach
255
Antonella Buccianti
18.1
Introduction
255
18.2
Geochemical Processes and Log-Ratio Approach
256
18.3
Log-Ratio Approach and Water Chemistry
258
18.4
Log-Ratio Approach and Volcanic Gas Chemistry
261
18.5
Log-Ratio Approach and Subducting Sediment Composition
263
18.6
Conclusions
265
Acknowledgements
265
References
265
19
Compositional Data Analysis in Planetology: The Surfaces of Mars
and Mercury
267
Helmut
Lammer,
Peter
Würz, Josep
Antoni
Martín-Fernández
and
Herbert Iwo Maria Lichtenegger
19.1
Introduction
267
19.1.1
Mars
267
19.1.2
Mercury
269
19.1.3
Analysis of Surface Composition
270
19.2
Compositional Analysis of Mars Surface
270
19.3
Compositional Analysis of Mercury s Surface
274
19.4
Conclusion
278
Acknowledgement
278
References
278
20
Spectral Analysis of Compositional Data in Cyclostratigraphy
282
Eulogio Pardo-lgúzquiza
and Javier
Heredia
20.1
Introduction
282
20.2
The Method
283
20.3
Case Study
285
20.4
Discussion
287
20.5
Conclusions
288
Acknowledgement
288
References
288
xiv CONTENTS
21
Multivariate Geochemical Data
Analysis in Physical Geography
290
Jennifer McKinley and Christopher David Lloyd
21.1
Introduction
290
21.2
Context
291
21.3 Data
293
21.4
Analysis
295
21.5
Discussion
299
21.6
Conclusion
300
Acknowledgement
300
References
300
22
Combining
Isotopie
and Compositional Data: A Discrimination of Regions
Prone to Nitrate Pollution
302
Roger Puig, Raimon Tolosana-Delgado,
Neus
Otero
and Albert Folch
22.1
Introduction
302
22.2
Study Area
303
22.2.1
Maresme
304
22.2.2
Osona
305
22.2.3
Lluçanès
305
22.2.4
Empordà
306
22.2.5
Selva
306
22.3
Analytical Methods
306
22.4
Statistical Treatment
307
22.4.1
Data Scaling
307
22.4.2
Linear Discriminant Analysis
309
22.4.3
Discriminant Biplots
310
22.5
Results and Discussion
311
22.6
Conclusions
314
Acknowledgements
315
References
315
23
Applications in Economics
318
Tim Fry
23.1
Introduction
318
23.2
Consumer Demand Systems
319
23.3
Miscellaneous Applications
322
23.4
Compositional Time Series
323
23.5
New Directions
323
23.6
Conclusion
325
References
325
Part V Software
327
24
Exploratory Analysis Using CoDaPack
3D 329
Santiago
Thió-Henestrosa andJosep
Daunis-i-Estadella
24.1
CoDaPack
3D
Description
329
24.2
Data Set Description
331
CONTENTS xv
24.3
Exploratory Analysis
333
24.3.1
Numerical Analysis
333
24.3.2
Biplot
334
24.3.3
The Ternary Diagram
335
24.3.4
Principal Component Analysis
336
24.3.5
Balance-Dendrogram
336
24.3.6
By Groups Description
338
24.4
Summary and Conclusions
339
Acknowledgements
340
References
340
25
robCompositions: An R-package for Robust Statistical Analysis
of Compositional Data
341
Matthias
Templ, Karel Hron
and Peter
Filzmoser
25.1
General Information on the R-package robCompositions
341
25.1.1
Data Sets Included in the Package
342
25.1.2
Design Principles
343
25.2
Expressing Compositional Data in Coordinates
343
25.3
Multivanate Statistical Methods for Compositional Data
Containing Outliers
345
25.3.1
Multivanate Outlier Detection
345
25.3.2
Principal Component Analysis and the Robust
Compositional Biplot
347
25.3.3
Discriminant Analysis
350
25.4
Robust Imputation of Missing Values
351
25.5
Summary
354
References
354
26
Linear Models with Compositions in
R
356
Raimon Tolosana-Delgado and Karl Gerald van den Boogaart
26.1
Introduction
356
26.2
The Illustration Data Set
357
26.2.1
The Data
357
26.2.2
Descriptive Analysis of Compositional Characteristics
358
26.3
Explanatory Binary Variable
360
26.4
Explanatory Categorical Variable
363
26.5
Explanatory Continuous Variable
365
26.6
Explanatory Composition
367
26.7
Conclusions
370
Acknowledgement
371
References
371
Index
373
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV039650280 |
| callnumber-first | Q - Science |
| callnumber-label | QA278 |
| callnumber-raw | QA278 |
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| ctrlnum | (OCoLC)785827980 (DE-599)BVBBV039650280 |
| dewey-full | 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/35 |
| dewey-search | 519.5/35 |
| dewey-sort | 3519.5 235 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV039650280 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:08:16Z |
| institution | BVB |
| isbn | 9780470711354 |
| language | English |
| lccn | 2011012322 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024499967 |
| oclc_num | 785827980 |
| open_access_boolean | |
| owner | DE-11 DE-355 DE-BY-UBR DE-Aug7 |
| owner_facet | DE-11 DE-355 DE-BY-UBR DE-Aug7 |
| physical | XXI, 378 S. Ill., graph. Darst., Kt. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Wiley |
| record_format | marc |
| spelling | Compositional data analysis theory and applications ed. by Vera Pawlowsky-Glahn ... Hoboken, N.J. Wiley 2011 XXI, 378 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Multivariate analysis Correlation (Statistics) Datenanalyse (DE-588)4123037-1 gnd rswk-swf Geostatistik (DE-588)4020279-3 gnd rswk-swf Korrelation (DE-588)4165343-9 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s Korrelation (DE-588)4165343-9 s Geostatistik (DE-588)4020279-3 s DE-604 Pawlowsky-Glahn, Vera Sonstige oth Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024499967&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Compositional data analysis theory and applications Multivariate analysis Correlation (Statistics) Datenanalyse (DE-588)4123037-1 gnd Geostatistik (DE-588)4020279-3 gnd Korrelation (DE-588)4165343-9 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4020279-3 (DE-588)4165343-9 |
| title | Compositional data analysis theory and applications |
| title_auth | Compositional data analysis theory and applications |
| title_exact_search | Compositional data analysis theory and applications |
| title_full | Compositional data analysis theory and applications ed. by Vera Pawlowsky-Glahn ... |
| title_fullStr | Compositional data analysis theory and applications ed. by Vera Pawlowsky-Glahn ... |
| title_full_unstemmed | Compositional data analysis theory and applications ed. by Vera Pawlowsky-Glahn ... |
| title_short | Compositional data analysis |
| title_sort | compositional data analysis theory and applications |
| title_sub | theory and applications |
| topic | Multivariate analysis Correlation (Statistics) Datenanalyse (DE-588)4123037-1 gnd Geostatistik (DE-588)4020279-3 gnd Korrelation (DE-588)4165343-9 gnd |
| topic_facet | Multivariate analysis Correlation (Statistics) Datenanalyse Geostatistik Korrelation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024499967&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pawlowskyglahnvera compositionaldataanalysistheoryandapplications |