Canonical analysis: a review with applications in ecology
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
Springer
1985
|
| Series: | Biomathmatics
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 351 S. |
| ISBN: | 3540136177 0387136177 |
Staff View
MARC
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| 100 | 1 | |a Gittins, Robert |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Canonical analysis |b a review with applications in ecology |c R. Gittins |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1985 | |
| 300 | |a XVI, 351 S. | ||
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| 490 | 1 | |a Biomathmatics |v 12 | |
| 650 | 7 | |a Canonische analyse |2 gtt | |
| 650 | 4 | |a Corrélation canonique (Statistique) | |
| 650 | 4 | |a Écologie - Méthodes statistiques | |
| 650 | 4 | |a Ökologie | |
| 650 | 4 | |a Canonical correlation (Statistics) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Introduction 1
1.1 The study of relationships 1
1.2 Objectives 3
1.3 Canonical analysis: overview 4
PARTI. THEORY 11
2. Canonical correlations and canonical variates 13
2.1 Introduction 13
2.2 Formulation 13
2.3 Derivation of canonical correlation coefficients and canonical
variates 15
2.3.1 Eigenanalysis 15
2.3.2 Singular value decompositon 17
2.3.3 Other derivations 18
2.3.4 Concluding remarks 20
2.4 Properties of canonical correlation coefficients, weights and
variates 22
2.4.1 Properties of canonical correlation coefficients 22
2.4.2 Properties of canonical weights 25
2.4.3 Properties of canonical variates 27
2.5 Computation 31
2.5.1 Numerical methods 31
2.5.2 Further remarks 35
3. Extensions and generalizations 37
3.1 Introduction 37
3.2 Further interpretive devices 37
3.2.1 Correlations between canonical variates and the original
variables 38
3.2.2 Variance extracted by a canonical variate 40
3.2.3 Redundancy 40
3.2.4 Total redundancy 41
XII Contents
3.2.5 Variable communalities 42
3.2.6 Concluding remarks 43
3.3 Extensions and generalizations 45
3.3.1 Redundancy analysis: an alternative to canonical
analysis 45
3.3.2 Improving the interpretability of canonical weights ... 45
3.3.3 Rotation of canonical variates 50
3.3.4 Validation 50
3.3.5 Predicting a criterion of maximum utility 52
3.3.6 Generalizations of canonical analysis 53
3.3.7 Concluding remarks 55
3.4 Hypothesis testing 56
3.4.1 Independence 56
3.4.2 Dimensionality 59
3.4.3 The contribution of particular variables 62
3.4.4 Hypothesis tests for nonnormal data 63
3.4.5 Residuals from a fitted model 63
4. Canonical variate analysis 67
4.1 Introduction 67
4.2 Binary valued dummy variables 68
4.3 Formulation and derivation 69
4.3.1 Point conceptualizations of NXp and NZg 70
4.3.2 Derivation 73
4.4 Further aspects of canonical variate analysis 75
4.5 Hypothesis testing 80
4.5.1 Equality of g vector means 81
4.5.2 Dimensionality 81
4.6 Affinities with other methods 82
4.6.1 Canonical variate analysis, multivariate analysis
of variance and multiple discriminant analysis 82
4.6.2 Canonical variate analysis and principal component
analysis 87
4.7 Imposition of structure 88
4.7.1 Designed comparisons 89
4.7.2 Separating the sources of variation 90
4.7.3 Further comments 91
4.8 Concluding remarks 92
5. Dual scaling 96
5.1 Introduction 96
5.2 Formulation and derivation 98
5.2.1 Maximizing the correlation between rows and columns 99
5.2.2 Maximizing the separation between rows and columns 103
Contents XIII
5.3 Further aspects of dual scaling 107
5.4 Hypothesis testing 113
5.4.1 Independence 113
5.4.2 Dimensionality 114
5.5 Affinities with other methods 115
5.5.1 Dual scaling and the analysis of contingency tables . . . 115
5.5.2 Dual scaling, correspondence analysis and principal
component analysis 119
5.6 Relationships among statistical methods 121
5.7 Concluding remarks 124
PART II. APPLICATIONS 127
General introduction 129
6. Experiment 1: an investigation of spatial variation 131
6.1 Introduction 131
6.2 Results 132
6.2.1 The canonical correlation coefficients 132
6.2.2 Independence 133
6.2.3 Dimensionality 133
6.2.4 The canonical variates 133
6.2.5 Variable communalities 140
6.3 Conclusions 141
7. Experiment 2: soil species relationships in a limestone grassland
community 142
7.1 Introduction 142
7.2 Results 143
7.2.1 The canonical correlation coefficients 143
7.2.2 Independence 144
7.2.3 Dimensionality 144
7.2.4 The canonical variates 145
7.2.5 Variable communalities 150
7.3 Conclusions 151
8. Soil vegetation relationships in a lowland tropical rain forest . . . .154
8.1 Introduction 154
8.2 Results 155
8.2.1 The canonical correlation coefficients 155
8.2.2 Independence 156
8.2.3 Dimensionality 156
8.2.4 The canonical variates 158
8.2.5 Variable communalities 162
XIV Contents
8.3 Ecological assessment of the results 162
8.4 Conclusions 164
9. Dynamic status of a lowland tropical rain forest 165
9.1 Introduction 165
9.2 Results 167
9.2.1 The canonical correlation coefficients 167
9.2.2 Independence 167
9.2.3 Dimensionality 167
9.2.4 The canonical variates 168
9.2.5 Variable communalities 174
9.3 Ecological assessment of the results 174
9.4 Conclusions 175
10. The structure of grassland vegetation in Anglesey, North Wales . . .177
10.1 Introduction 177
10.2 Results 179
10.2.1 The canonical correlation coefficients 179
10.2.2 Equality of community centroids 179
10.2.3 Collinearity 179
10.2.4 The canonical variates 180
10.2.5 Variable communalities 183
10.3 Ecological assessment of the results 184
10.4 Conclusions 186
11. The nitrogen nutrition of eight grass species 188
11.1 Introduction 188
11.2 Multivariate analysis of variance 189
11.2.1 Results 189
11.2.2 Designed comparisons 193
11.3 Canonical variate analysis 198
11.3.1 Results 199
11.4 Relationships between multivariate analysis of variance,
discriminant analysis and canonical variate analysis 203
11.5 Ecological assessment of the results 204
11.6 Conclusions 206
12. Herbivore environment relationships in the Rwenzori National Park,
Uganda 207
12.1 Introduction 207
12.2 Contingency table analysis 209
12.2.1 Results 210
Contents XV
12.3 Dual scaling 212
12.3.1 Results 213
12.4 Relationships between contingency table analysis and dual
scaling 219
12.5 Ecological assessment of the results 220
12.6 Conclusions 224
PART III. APPRAISAL AND PROSPECT 227
13. Applications: assessment and conclusions 229
13.1 Introduction 229
13.2 Assessment 230
13.3 Conclusions 237
14. Research issues and future developments 238
14.1 Introduction 238
14.2 Data collection 239
14.2.1 Choice of variables 240
14.2.2 Experimental design 240
14.3 Initial data exploration 242
14.3.1 Homogeneity 242
14.3.2 Assessing joint distribution 245
14.3.3 Re expressing variables 250
14.4 Potential data problems 253
14.4.1 Outlying or influential observations 254
14.4.2 Long tailed distributions 256
14.4.3 Collinearity 260
14.5 Statistical assessment 266
14.5.1 Residuals in canonical analysis 266
14.5.2 Does the model fit? 267
14.5.3 Stability of results 274
14.5.4 Miscellanea 276
14.6 Concluding remarks 285
APPENDICES 289
A.1 Multivariate regression 291
A.2 Data sets used in worked applications 301
A.3 Species composition of a limestone grassland community 308
XVI Contents
References 309
Species index 333
Author index 335
Subject index 341
|
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| id | DE-604.BV000368294 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:12:58Z |
| institution | BVB |
| isbn | 3540136177 0387136177 |
| language | English |
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| physical | XVI, 351 S. |
| publishDate | 1985 |
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| series | Biomathmatics |
| series2 | Biomathmatics |
| spelling | Gittins, Robert Verfasser aut Canonical analysis a review with applications in ecology R. Gittins Berlin u.a. Springer 1985 XVI, 351 S. txt rdacontent n rdamedia nc rdacarrier Biomathmatics 12 Canonische analyse gtt Corrélation canonique (Statistique) Écologie - Méthodes statistiques Ökologie Canonical correlation (Statistics) Ecology Statistical methods Korrelationsanalyse (DE-588)4194560-8 gnd rswk-swf Korrelationsanalyse (DE-588)4194560-8 s DE-604 Biomathmatics 12 (DE-604)BV000894631 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000228588&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gittins, Robert Canonical analysis a review with applications in ecology Biomathmatics Canonische analyse gtt Corrélation canonique (Statistique) Écologie - Méthodes statistiques Ökologie Canonical correlation (Statistics) Ecology Statistical methods Korrelationsanalyse (DE-588)4194560-8 gnd |
| subject_GND | (DE-588)4194560-8 |
| title | Canonical analysis a review with applications in ecology |
| title_auth | Canonical analysis a review with applications in ecology |
| title_exact_search | Canonical analysis a review with applications in ecology |
| title_full | Canonical analysis a review with applications in ecology R. Gittins |
| title_fullStr | Canonical analysis a review with applications in ecology R. Gittins |
| title_full_unstemmed | Canonical analysis a review with applications in ecology R. Gittins |
| title_short | Canonical analysis |
| title_sort | canonical analysis a review with applications in ecology |
| title_sub | a review with applications in ecology |
| topic | Canonische analyse gtt Corrélation canonique (Statistique) Écologie - Méthodes statistiques Ökologie Canonical correlation (Statistics) Ecology Statistical methods Korrelationsanalyse (DE-588)4194560-8 gnd |
| topic_facet | Canonische analyse Corrélation canonique (Statistique) Écologie - Méthodes statistiques Ökologie Canonical correlation (Statistics) Ecology Statistical methods Korrelationsanalyse |
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