| Description |
1 online resource (xvii, 280 pages) : illustrations (some color) |
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text file |
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PDF |
| Series |
Springer series in statistics,
0172-7397
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Springer series in statistics,
0172-7397
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| Bibliography |
Includes bibliographical references and index. |
| Contents |
Intro; Preface; Acknowledgments; Contents; Acronyms; 1 Compositional Data as a Methodological Concept; 1.1 What Are Compositional Data?; 1.2 Introductory Problems; 1.2.1 PhD Students Example; 1.2.2 Beer Data Example; 1.2.3 Geochemical Data Example; 1.3 Principles of Compositional Data Analysis; 1.4 Steps to a Concise Methodology; References; 2 Analyzing Compositional Data Using R; 2.1 Brief Overview on Packages Related to Compositional Data Analysis; 2.1.1 compositions; 2.1.2 robCompositions; 2.1.3 ggtern; 2.1.4 zCompositions; 2.1.5 mvoutlier, StatDA; 2.1.6 CoDaPack; 2.1.7 compositionsGUI. |
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2.2 The Statistics Environment R2.3 Basics in R; 2.3.1 Installation of R and Updates; 2.3.2 Install robCompositions; 2.3.3 Help; 2.3.4 The R Workspace and the Working Directory; 2.3.5 Data Types; 2.3.6 Generic Functions, Methods and Classes; References; 3 Geometrical Properties of Compositional Data; 3.1 Motivation; 3.2 Aitchison Geometry on the Simplex; 3.3 Coordinate Representations of Compositions; 3.3.1 Additive Logratio (alr) Coordinates; 3.3.2 Centered Logratio (clr) Coefficients; 3.3.3 Isometric Logratio (ilr) and Pivot Coordinates. |
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3.3.4 Special Coordinate Systems: Generalization of Pivot Coordinates3.3.5 Special Coordinate Systems: Symmetric Pivot Coordinates; 3.3.6 Special Coordinate Systems: Balances; 3.4 Examples; References; 4 Exploratory Data Analysis and Visualization; 4.1 Descriptive Statistics of Compositional Data; 4.2 Univariate Graphics; 4.3 Bivariate Plotting; 4.4 Multivariate Visualization; References; 5 First Steps for a Statistical Analysis; 5.1 Distributions and Statistical Inference; 5.1.1 Normality Testing; 5.1.2 Statistical Inference in Coordinates; 5.2 Classical and Robust Statistical Analysis. |
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5.2.1 Univariate Location5.2.2 Univariate Scale; 5.2.3 Multivariate Location and Covariance; 5.2.4 Center and Variation Matrix; 5.3 Outlier Detection; 5.3.1 Univariate Outliers; 5.3.2 Multivariate Outliers; 5.3.3 Interpretation of Multivariate Outliers; 5.4 Example; References; 6 Cluster Analysis; 6.1 Distance Measures and Dissimilarities; 6.2 Hierarchical Clustering Methods; 6.2.1 Agglomerative Clustering Algorithms; 6.2.1.1 Single Linkage; 6.2.1.2 Complete Linkage; 6.2.1.3 Average Linkage; 6.2.1.4 Ward's Method; 6.2.2 Tree Cutting; 6.3 Partitioning Methods; 6.4 Model-Based Clustering. |
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6.5 Fuzzy Clustering6.6 Clustering Parts: Q-Mode Clustering; 6.7 Evaluation; 6.8 Examples; References; 7 Principal Component Analysis; 7.1 Introductory Remarks; 7.2 Estimation of Principal Components; 7.2.1 Estimation by SVD; 7.2.2 Estimation by Decomposing the Covariance Matrix; 7.3 Compositional Biplot; 7.4 Examples; 7.4.1 Representation of Principal Components in a Ternary Diagram; 7.4.2 Example: Household Expenditures at EU Level; 7.4.3 Example: Beer Data; 7.4.4 Example with Two Different Compositions; 7.4.5 Example for PCA Including External Non-compositional Variables; References. |
| Summary |
This book presents the statistical analysis of compositional data using the log-ratio approach. It includes a wide range of classical and robust statistical methods adapted for compositional data analysis, such as supervised and unsupervised methods like PCA, correlation analysis, classification and regression. In addition, it considers special data structures like high-dimensional compositions and compositional tables. The methodology introduced is also frequently compared to methods which ignore the specific nature of compositional data. It focuses on practical aspects of compositional data analysis rather than on detailed theoretical derivations, thus issues like graphical visualization and preprocessing (treatment of missing values, zeros, outliers and similar artifacts) form an important part of the book. Since it is primarily intended for researchers and students from applied fields like geochemistry, chemometrics, biology and natural sciences, economics, and social sciences, all the proposed methods are accompanied by worked-out examples in R using the package robCompositions.-- Provided by publisher. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Mathematical statistics.
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Geochemistry. |
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Mathematical & statistical software. |
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Probability & statistics. |
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Social research & statistics. |
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MATHEMATICS -- Applied. |
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MATHEMATICS -- Probability & Statistics -- General. |
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EstadÃstica matemática |
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Mathematical statistics |
| Added Author |
Hron, Karel, author.
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Templ, Matthias, author.
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| Other Form: |
Print version: 3319964208 9783319964201 (OCoLC)1041498517 |
| ISBN |
9783319964225 (electronic bk.) |
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3319964224 (electronic bk.) |
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9783319964201 (print) |
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3319964208 |
| Standard No. |
10.1007/978-3-319-96422-5 |
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