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BL
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| Record Number
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878097
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| Main Entry
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Greenacre, Michael J.
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| Title & Author
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Compositional data analysis in practice /\ Michael Greenacre.
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| Publication Statement
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Boca Raton, Florida :: CRC Press,, [2018]
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| Series Statement
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Chapman & Hall/CRC interdisciplinary statistics
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| Page. NO
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1 online resource
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| ISBN
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042984901X
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: 0429849028
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: 9780429849015
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: 9780429849022
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1138316431
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113831661X
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9781138316430
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9781138316614
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| Contents
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Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; 1 What are compositional data, and why are they special?; 1.1 Examples of compositional data; 1.2 Why are compositional data different from other types of data?; 1.3 Basic terminology and notation in compositional data analysis; 1.4 Basic principles of compositional data analysis; 1.5 Ratios and logratios; 2 Geometry and visualization of compositional data; 2.1 Simple graphics; 2.2 Geometry in a simplex; 2.3 Moving out of the simplex; 2.4 Distances between points in logratio space.
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3 Logratio transformations3.1 Additive logratio transformations; 3.2 Centred logratio transformations; 3.3 Logratios incorporating amalgamations; 3.4 Isometric logratio transformations; 3.5 Comparison of logratios in practice; 3.6 Practical interpretation of logratios; 4 Properties and distributions of logratios; 4.1 Lognormal distribution; 4.2 Logit function; 4.3 Additive logistic normal distribution; 4.4 Logratio variances and covariances; 4.5 Testing for multivariate normality; 4.6 When logratios are not normal; 5 Regression models involving compositional data.
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5.1 Visualizing ratios as a graph5.2 Using simple logratios as predictors; 5.3 Compositions as responses -- total logratio variance; 5.4 Redundancy analysis; 6 Dimension reduction using logratio analysis; 6.1 Weighted principal component analysis; 6.2 Logratio analysis; 6.3 Different biplot scaling options; 6.4 Constrained compositional biplots; 7 Clustering of compositional data; 7.1 Logratio distances between rows and between columns; 7.2 Clustering based on logratio distances; 7.3 Weighted Ward clustering; 7.4 Isometric logratio versus amalgamation balances.
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8 Problem of zeros, with some solutions8.1 Zero replacement; 8.2 Sensitivity to zero replacement; 8.3 Subcompositional incoherence; 8.4 Correspondence analysis alternative; 9 Simplifying the task: variable selection; 9.1 Explaining total logratio variance; 9.2 Stepwise selection of logratios; 9.3 Parsimonious variable selection; 9.4 Amalgamation logratios as variables for selection; 9.5 Signal and noise in compositional data; 10 Case study: Fatty acids of marine amphipods; 10.1 Introduction; 10.2 Material and methods; 10.3 Results; 10.4 Discussion and conclusion.
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A Appendix: Theory of compositional data analysisA. 1 Basic notation; A.2 Ratios and logratios; A.3 Logratio distance; A.4 Logratio variance; A.5 Logratio analysis (LRA); A.6 Principal component analysis (PCA); A.7 Procrustes analysis; A.8 Constrained logratio analysis and redundancy analysis; A.9 Permutation tests; A.10 Weighted Ward clustering; B Appendix: Bibliography of compositional data analysis; B.1 Books; B.2 Articles; B.3 Web resources; C Appendix: Computation of compositional data analysis; C.1 Simple graphics for compositional data; C.2 Logratio transformations.
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| Abstract
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Compositional Data Analysis in Practice is a user-oriented practical guide to the analysis of data with the property of a constant sum, for example percentages adding up to 100%. Compositional data can give misleading results if regular statistical methods are applied, and are best analysed by first transforming them to logarithms of ratios. This book explains how this transformation affects the analysis, results and interpretation of this very special type of data. All aspects of compositional data analysis are considered: visualization, modelling, dimension-reduction, clustering and variable selection, with many examples in the fields of food science, archaeology, sociology and biochemistry, and a final chapter containing a complete case study using fatty acid compositions in ecology. The applicability of these methods extends to other fields such as linguistics, geochemistry, marketing, economics and finance. R SoftwareThe R package easyCODA, which accompanies this book, can be downloaded from R-Forge as follows: install.packages and will be available on CRAN soon. Notice that the R packages ca and vegan also have to be installed (from CRAN in the usual way).
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| Subject
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Electronic data processing.
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Principal components analysis.
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Quantitative research.
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Electronic data processing.
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MATHEMATICS-- Probability Statistics-- General.
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Principal components analysis.
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| Subject
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Quantitative research.
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| Dewey Classification
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001.42
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| LC Classification
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QA76.9.Q36 .G74 2019
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