Modeling and analysis of compositional data:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2015
|
| Edition: | 1. ed. |
| Series: | Statistics in practice
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 247 S. Ill., graph. Darst. |
| ISBN: | 9781118443064 |
Staff View
MARC
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| 245 | 1 | 0 | |a Modeling and analysis of compositional data |c Vera Pawlowsky-Glahn ; Juan José Egozcue ; Raimon Tolosana-Delgado |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2015 | |
| 300 | |a XVII, 247 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Statistics in practice | |
| 650 | 4 | |a Multivariate analysis | |
| 650 | 4 | |a Geometric analysis | |
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| 700 | 1 | |a Tolosana-Delgado, Raimon |d 1976- |e Verfasser |0 (DE-588)106955331X |4 aut | |
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Record in the Search Index
| _version_ | 1818858758354239488 |
|---|---|
| adam_text |
Contents
Preface
xl
About the Authors
xv
Acknowledgments
xix
1
Introduction I
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 A itch
ison
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
I 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
viii CONTENTS
4.7 Additive logratio
coordinates (air)
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 Sv: endomorphisms
55
4.9.3
Other matrix transformations on 5D: 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 ID 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
Statistkal
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
CONTENTS
ix
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
В
Random Variables
228
B.I Probability spaces and random variables
228
B.2 Description of probability
232
List of Abbreviations and Symbols
234
Author Index
237
General Index
241 |
| any_adam_object | 1 |
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| author_GND | (DE-588)106954566X (DE-588)1069546402 (DE-588)106955331X |
| author_facet | Pawlowsky-Glahn, Vera Egozcue, Juan José 1950- Tolosana-Delgado, Raimon 1976- |
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| bvnumber | BV042508282 |
| classification_rvk | SK 850 |
| ctrlnum | (OCoLC)908617600 (DE-599)HBZHT018530549 |
| discipline | Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV042508282 |
| illustrated | Illustrated |
| indexdate | 2024-12-19T09:01:22Z |
| institution | BVB |
| isbn | 9781118443064 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027942856 |
| oclc_num | 908617600 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-11 |
| owner_facet | DE-473 DE-BY-UBG DE-11 |
| physical | XVII, 247 S. Ill., graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Wiley |
| record_format | marc |
| series2 | Statistics in practice |
| spelling | Pawlowsky-Glahn, Vera Verfasser (DE-588)106954566X aut Modeling and analysis of compositional data Vera Pawlowsky-Glahn ; Juan José Egozcue ; Raimon Tolosana-Delgado 1. ed. Chichester Wiley 2015 XVII, 247 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics in practice Multivariate analysis Geometric analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Geometrische Analysis (DE-588)4156708-0 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 s Statistik (DE-588)4056995-0 s Geometrische Analysis (DE-588)4156708-0 s DE-604 Egozcue, Juan José 1950- Verfasser (DE-588)1069546402 aut Tolosana-Delgado, Raimon 1976- Verfasser (DE-588)106955331X aut Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027942856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pawlowsky-Glahn, Vera Egozcue, Juan José 1950- Tolosana-Delgado, Raimon 1976- Modeling and analysis of compositional data Multivariate analysis Geometric analysis Multivariate Analyse (DE-588)4040708-1 gnd Geometrische Analysis (DE-588)4156708-0 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4156708-0 (DE-588)4056995-0 |
| title | Modeling and analysis of compositional data |
| title_auth | Modeling and analysis of compositional data |
| title_exact_search | Modeling and analysis of compositional data |
| title_full | Modeling and analysis of compositional data Vera Pawlowsky-Glahn ; Juan José Egozcue ; Raimon Tolosana-Delgado |
| title_fullStr | Modeling and analysis of compositional data Vera Pawlowsky-Glahn ; Juan José Egozcue ; Raimon Tolosana-Delgado |
| title_full_unstemmed | Modeling and analysis of compositional data Vera Pawlowsky-Glahn ; Juan José Egozcue ; Raimon Tolosana-Delgado |
| title_short | Modeling and analysis of compositional data |
| title_sort | modeling and analysis of compositional data |
| topic | Multivariate analysis Geometric analysis Multivariate Analyse (DE-588)4040708-1 gnd Geometrische Analysis (DE-588)4156708-0 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Multivariate analysis Geometric analysis Multivariate Analyse Geometrische Analysis Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027942856&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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