Applied Multivariate Statistics with R

Now in its second edition, this book brings multivariate statistics to graduate-level practitioners, making these analytical methods accessible without lengthy mathematical derivations. Using the open source shareware program R , Dr. Zelterman demonstrates the process and outcomes for a wide array of multivariate statistical applications. Chapters cover graphical displays; linear algebra; univariate, bivariate and multivariate normal distributions; factor methods; linear regression; discrimination and classification; clustering; time series models; and additional methods. He uses practical examples from diverse disciplines, to welcome readers from a variety of academic specialties. Each chapter includes exercises, real data sets, and R implementations. The book avoids theoretical derivations beyond those needed to fully appreciate the methods. Prior experience with R is not necessary. New to this edition are chapters devoted to longitudinal studies and the clustering of large data. It is an excellent resource for students of multivariate statistics, as well as practitioners in the health and life sciences who are looking to integrate statistics into their work. Permissions In Addition Grant Support Preface to the Second Edition Preface to the First Edition Acknowledgments Contents About the Author 1 Introduction 1.1 Goals of Multivariate Statistical Techniques 1.2 Data Reduction or Structural Simplification 1.3 Grouping and Classifying Observations 1.4 Examination of Dependence Among Variables 1.5 Describing Relationships Between Groups of Variables 1.6 Hypothesis Formulation and Testing 1.7 Multivariate Graphics and Distributions 1.8 Why R? 1.9 Additional Readings 2 Elements of R 2.1 Getting Started in R 2.1.1 R as a Calculator 2.1.2 Vectors in R 2.1.3 Printing in R 2.2 Simulation and Simple Statistics 2.3 Handling Data Sets 2.4 Basic Data Manipulation and Statistics 2.5 Programming and Writing Functions in R 2.6 A Larger Simulation 2.7 Advanced Numerical Operations 2.8 Housekeeping 2.9 Exercises 3 Graphical Displays 3.1 Graphics in R 3.2 Displays for Univariate Data 3.3 Displays for Bivariate Data 3.3.1 Plot Options, Colors, and Characters 3.3.2 More Graphics for Bivariate Data 3.4 Displays for Three-Dimensional Data 3.5 Displays for Higher Dimensional Data 3.5.1 Pairs, Bagplot, Coplot, and Corrplot 3.5.2 Glyphs: Stars, Radar, and Faces 3.5.3 Parallel Coordinates 3.6 Additional Reading 3.7 Exercises 4 Some Linear Algebra 4.1 Apples and Oranges 4.2 Vectors 4.3 Basic Matrix Arithmetic 4.4 Matrix Operations in R 4.5 Advanced Matrix Operations 4.5.1 Determinants 4.5.2 Matrix Inversion 4.5.3 Eigenvalues and Eigenvectors 4.5.4 Diagonalizable Matrices 4.5.5 Generalized Inverses 4.5.6 Matrix Square Root 4.6 Exercises 5 The Univariate Normal Distribution 5.1 The Normal Density and Distribution Functions 5.2 Relationship to Other Distributions 5.3 Transformations to Normality 5.4 Tests for Normality 5.5 Inference on Univariate Normal Means 5.6 Inference on Variances 5.7 Maximum Likelihood Estimation, Part I 5.8 Exercises 6 Bivariate Normal Distribution 6.1 The Bivariate Normal Density Function 6.2 Properties of the Bivariate Normal Distribution 6.3 Inference on Bivariate Normal Parameters 6.4 Tests for Bivariate Normality 6.5 Maximum Likelihood Estimation, Part II 6.6 Exercises 7 Multivariate Normal Distribution 7.1 Multivariate Normal Density and Its Properties 7.2 Inference on Multivariate Normal Means 7.3 Example: Home Price Index 7.4 Maximum Likelihood, Part III: Models for Means 7.5 Inference on Multivariate Normal Variances 7.6 Fitting Patterned Covariance Matrices 7.7 Tests for Multivariate Normality 7.8 Exercises 8 Factor Methods 8.1 Principal Component Analysis 8.2 Example 1: Investment Allocations 8.3 Example 2: Kuiper Belt Objects 8.4 Example 3: Health Outcomes in US Hospitals 8.5 Factor Analysis 8.6 Confirmatory Factor Analysis 8.7 Path Analysis 8.8 Structural Equations and Latent Growth Modeling 8.9 Exercises 9 Multivariable Linear Regression 9.1 Univariate Regression 9.2 Multivariable Regression in R 9.3 A Large Health Survey 9.4 Penalized Linear Regression 9.5 Exercises 10 Discrimination and Classification 10.1 Logistic Regression 10.2 Penalized Logistic Regression 10.3 Several Categorical Groups 10.4 Multinomial Logistic Regression 10.5 Linear Discriminant Analysis 10.6 Support Vector Machine 10.7 Regression Trees 10.8 Exercises 11 Clustering Methods 11.1 Hierarchical Clustering 11.2 K-Means Clustering 11.3 Diagnostics and Validation 11.4 Clustering Application: Image Processing 11.5 Gaussian Mixture Model and the EM Algorithm 11.6 DBscan 11.7 Exercises 12 Basic Models for Longitudinal Data 12.1 Marginal Models 12.2 Transitional Models 12.3 Missing Values 12.4 Semiparametric Modeling with GEE 12.5 Exercises 13 Time Series Models 13.1 Introductory Examples and Simple Analyses 13.2 Autoregressive Models 13.3 Spectral Decomposition 13.4 Exercises 14 Other Useful Methods 14.1 Ranking From Paired Comparisons 14.2 Canonical Correlations 14.3 Mediation 14.4 Counterfactuals 14.5 Methods for Extreme Order Statistics 14.6 Methods for Overdispersion 14.7 Big Data and Wide Data 14.8 Exercises Appendix A R Libraries Used Appendix Selected Solutions and Hints Appendix References Index