Multivariate Statistical Methods : A Primer, Fourth Edition

This work provides an introductory overview of multivariate methods without getting too deep into the mathematical details. This edition retains the clear and concise style of the previous editions and focuses on examples from biological and environmental sciences. Multivariate Statistical Methods: A Primer provides an introductory overview of multivariate methods without getting too deep into the mathematical details. This fourth edition is a revised and updated version of this bestselling introductory textbook. It retains the clear and concise style of the previous editions of the book and focuses on examples from biological and environmental sciences. The major update with this edition is that R code has been included for each of the analyses described, although in practice any standard statistical package can be used. The original idea with this book still applies. This was to make it as short as possible and enable readers to begin using multivariate methods in an intelligent manner. With updated information on multivariate analyses, new references, and R code included, this book continues to provide a timely introduction to useful tools for multivariate statistical analysis MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Dedication 6 Contents 10 Preface 14 Authors 16 Chapter 1 The material of multivariate analysis 18 1.1 Examples of multivariate data 18 1.2 Preview of multivariate methods 27 1.3 The multivariate normal distribution 31 1.4 Computer programs 32 References 32 Appendix: An Introduction to R 33 References 44 Chapter 2 Matrix algebra 46 2.1 The need for matrix algebra 46 2.2 Matrices and vectors 46 2.3 Operations on matrices 48 2.4 Matrix inversion 50 2.5 Quadratic forms 51 2.6 Eigenvalues and eigenvectors 51 2.7 Vectors of means and covariance matrices 52 2.8 Further reading 54 References 54 Appendix: Matrix Algebra in R 55 Chapter 3 Displaying multivariate data 58 3.1 The problem of displaying many variables in two dimensions 58 3.2 Plotting index variables 58 3.3 The draftsman’s plot 60 3.4 The representation of individual data points 61 3.5 Profiles of variables 63 3.6 Discussion and further reading 64 References 65 Appendix: Producing Plots in R 66 References 68 Chapter 4 Tests of significance with multivariate data 70 4.1 Simultaneous tests on several variables 70 4.2 Comparison of mean values for two samples: The single-variable case 70 4.3 Comparison of mean values for two samples: The multivariate case 72 4.4 Multivariate versus univariate tests 76 4.5 Comparison of variation for two samples: The single-variable case 77 4.6 Comparison of variation for two samples: The multivariate case 78 4.7 Comparison of means for several samples 83 4.8 Comparison of variation for several samples 87 4.9 Computer programs 91 References 95 Appendix: Tests of Significance in R 96 References 98 Chapter 5 Measuring and testing multivariate distances 100 5.1 Multivariate distances 100 5.2 Distances between individual observations 100 5.3 Distances between populations and samples 103 5.4 Distances based on proportions 108 5.5 Presence-absence data 109 5.6 The Mantel randomization test 110 5.7 Computer programs 114 5.8 Discussion and further reading 114 References 115 Appendix: Multivariate distance measures in R 117 References 118 Chapter 6 Principal components analysis 120 6.1 Definition of principal components 120 6.2 Procedure for a principal components analysis 121 6.3 Computer programs 130 6.4 Further reading 131 References 134 Appendix: Principal Components Analysis (PCA) in R 135 References 136 Chapter 7 Factor analysis 138 7.1 The factor analysis model 138 7.2 Procedure for a factor analysis 141 7.3 Principal components factor analysis 143 7.4 Using a factor analysis program to do principal components analysis 145 7.5 Options in analyses 150 7.6 The value of factor analysis 151 7.7 Discussion and further reading 151 References 152 Appendix: Factor Analysis in R 153 References 154 Chapter 8 Discriminant function analysis 156 8.1 The problem of separating groups 156 8.2 Discrimination using Mahalanobis distances 156 8.3 Canonical discriminant functions 157 8.4 Tests of significance 159 8.5 Assumptions 160 8.6 Allowing for prior probabilities of group membership 165 8.7 Stepwise discriminant function analysis 167 8.8 Jackknife classification of individuals 167 8.9 Assigning ungrouped individuals to groups 168 8.10 Logistic regression 168 8.11 Computer programs 173 8.12 Discussion and further reading 174 References 174 Appendix: Discriminant Function Analysis in R 176 References 179 Chapter 9 Cluster analysis 180 9.1 Uses of cluster analysis 180 9.2 Types of cluster analysis 180 9.3 Hierarchic methods 181 9.4 Problems with cluster analysis 183 9.5 Measures of distance 184 9.6 Principal components analysis with cluster analysis 185 9.7 Computer programs 189 9.8 Discussion and further reading 190 References 194 Appendix: Cluster Analysis in R 195 Reference 196 Chapter 10 Canonical correlation analysis 198 10.1 Generalizing a multiple regression analysis 198 10.2 Procedure for a canonical correlation analysis 200 10.3 Tests of significance 201 10.4 Interpreting canonical variates 202 10.5 Computer programs 214 10.6 Further reading 214 References 216 Appendix: Canonical Correlation in R 217 References 218 Chapter 11 Multidimensional scaling 220 11.1 Constructing a map from a distance matrix 220 11.2 Procedure for multidimensional scaling 221 11.3 Computer programs 231 11.4 Further reading 231 References 232 Appendix: Multidimensional scaling in R 233 References 234 Chapter 12 Ordination 236 12.1 The ordination problem 236 12.2 Principal components analysis 237 12.3 Principal coordinates analysis 242 12.4 Multidimensional scaling 248 12.5 Correspondence analysis 250 12.6 Comparison of ordination methods 255 12.7 Computer programs 256 12.8 Further reading 256 References 257 Appendix: Ordination methods in R 258 References 260 Chapter 13 Epilogue 262 13.1 The next step 262 13.2 Some general reminders 262 13.3 Missing values 263 References 264 Index 266