Applied Compositional Data Analysis: With Worked Examples in R

Description

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. Front Matter ....Pages i-xvii Compositional Data as a Methodological Concept (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 1-16 Analyzing Compositional Data Using R (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 17-34 Geometrical Properties of Compositional Data (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 35-68 Exploratory Data Analysis and Visualization (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 69-83 First Steps for a Statistical Analysis (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 85-106 Cluster Analysis (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 107-130 Principal Component Analysis (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 131-148 Correlation Analysis (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 149-162 Discriminant Analysis (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 163-179 Regression Analysis (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 181-205 Methods for High-Dimensional Compositional Data (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 207-225 Compositional Tables (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 227-243 Preprocessing Issues (Peter Filzmoser, Karel Hron, Matthias Templ)....Pages 245-272 Back Matter ....Pages 273-280