Compositional data analysis in practice:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Florida
CRC Press
[2018]
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| Schriftenreihe: | Chapman & Hall/CRC interdisciplinary statistics series
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiv, 121 Seiten Illustrationen, Diagramme |
| ISBN: | 9781138316614 9781138316430 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents 1 2 Preface................................................................................................. xi What are compositional data, and why are they special?............................................................... 1 1.1 1.2 1.3 1.4 1.5 1 2 3 5 6 Geometry and visualization of compositional data .......................................................................... 2.1 2.2 2.3 2.4 3 4 Examples of compositional data.............................................. Why are compositional data different from other types of data? Basic terminology and notation in compositional data analysis Basic principles of compositional data analysis ........................ Ratios and logratios............................................. ....................... 9 Simple graphics .................................. ....................................... Geometry in a simplex ............................................................... Moving out of the simplex........................................................... Distances between points in logratio space ............................. 9 12 14 15 Logratio transformations................................................................. 17 3.1 3.2 3.3 3.4 3.5 3.6 Additive logratio transformations ............................................... Centred logratio transformations ....................... ............... Logratios incorporating amalgamations .................................. Isometric logratio transformations............................................. Comparison of logratios in
practice........................................... Practical interpretation of logratios ........................................... 17 18 19 19 21 23 Properties and distributions of logratios...................................... 25 4.1 4.2 4.3 4.4 25 27 27 28 Lognormal distribution................................................ Logit function............................................................................... Additive logistic normal distribution........................................... Logratio variances and covariances ......................................... ѴІІ
viii Contents 4.5 4.6 5 б 7 8 9 Testing for multivariate normality................................................ 30 When logratios are not normal................................................... 31 Regression models involving compositional data..................... 33 5.1 5.2 5.3 5.4 Visualizing ratios as a graph...................................................... Using simple logratios as predictors.......................................... Compositions as responses - total logratio variance............... Redundancy analysis ................................................................. 33 34 37 39 Dimension reduction using logratio analysis............................... 41 6.1 6.2 6.3 6.4 Weighted principal component analysis.................................... Logratio analysis.......................................................................... Different biplot scaling options................................................... Constrained compositional biplots............................................. 41 42 44 46 Clustering of compositional data................................................... 49 7.1 7.2 7.3 7.4 Logratio distances between rows and between columns......... Clustering based on logratio distances...................................... Weighted Ward clustering .................................... .................... Isometric logratio versus amalgamation balances.................... 49 50 50 53 Problem of zeros, with some solutions.......................................... 57 8.1 8.2 8.3 8.4 Zero
replacement........................................................................ Sensitivity to zero replacement................................................... Subcompositional incoherence................................................... Correspondence analysis alternative........................................ 57 58 59 60 Simplifying the task: variable selection........................................ 65 9.1 9.2 9.3 9.4 9.5 65 66 68 70 70 Explaining total logratio variance............................................... Stepwise selection of logratios................................................... Parsimonious variable selection................................................. Amalgamation logratios as variables for selection.................... Signal and noise in compositional data.................................... 10 Case study: Fatty acids of marine amphipods................................................... 73 10.1 10.2 10.3 10.4 Introduction .................................................................................. Material and methods................................................................. Results ......................................................................................... Discussion and conclusion.......................................................... 73 74 75 80
Contents A IX Appendix: Theory of compositional data analysis...................... 81 A.l Basic notation......................................................................... A.2 Ratios and logratios................................................................ A.3 Logratio distance ....................................................................... A.4 Logratio variance....................................................................... A.5 Logratio analysis (LRA).............................................................. A.6 Principal componentanalysis (PCA)......................................... A.7 Procrustes analysis.................................................................... A.8 Constrained logratioanalysis and redundancy analysis.......... A.9 Permutation tests........................................................................ A.10 Weighted Ward clustering .......................................................... В Appendix: Bibliography of compositional data analysis........... 91 B.l В .2 B.3 C 81 82 85 85 86 87 88 89 89 90 Books........................................................................................... 91 Articles ....................................................................................... 92 Web resources ........................................................................... 95 Appendix: Computation of compositional data analysis........... 97 C.l C.2 C.3 C.4 Simple graphics for compositional data................................... 97 Logratio
transformations............................................................ 98 Compositional data modelling.....................................................102 Compositional data analytics.......................................................103 D Appendix: Glossary of terms....................................................... Ill E Appendix: Epilogue .......................................................................... 115 Index 119
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| indexdate | 2024-07-10T08:20:42Z |
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| isbn | 9781138316614 9781138316430 |
| language | English |
| lccn | 018017447 |
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| spelling | Greenacre, Michael J. 1951- (DE-588)170432300 aut Compositional data analysis in practice by Michael Greenacre Boca Raton, Florida CRC Press [2018] xiv, 121 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC interdisciplinary statistics series Includes bibliographical references and index Quantitative research Principal components analysis Electronic data processing Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030915862&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Greenacre, Michael J. 1951- Compositional data analysis in practice Quantitative research Principal components analysis Electronic data processing Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Compositional data analysis in practice |
| title_auth | Compositional data analysis in practice |
| title_exact_search | Compositional data analysis in practice |
| title_full | Compositional data analysis in practice by Michael Greenacre |
| title_fullStr | Compositional data analysis in practice by Michael Greenacre |
| title_full_unstemmed | Compositional data analysis in practice by Michael Greenacre |
| title_short | Compositional data analysis in practice |
| title_sort | compositional data analysis in practice |
| topic | Quantitative research Principal components analysis Electronic data processing Statistik (DE-588)4056995-0 gnd |
| topic_facet | Quantitative research Principal components analysis Electronic data processing Statistik |
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