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Table of 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
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
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
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
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
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
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
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
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