Compositional Data Analysis in Practice 论文

摘要

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 -- 3 Logratio transformations -- 3.1 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 -- 5.1 Visualizing ratios as a graph -- 5.2 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 -- 8 Problem of zeros, with some solutions -- 8.1 Zero replacement