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Multivariate Statistical Methods: A Primer
288![Multivariate Statistical Methods: A Primer](http://img.images-bn.com/static/redesign/srcs/images/grey-box.png?v11.8.5)
Multivariate Statistical Methods: A Primer
288Hardcover(5th ed.)
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Overview
Multivariate Statistical Methods: A Primer offers an introduction to multivariate statistical methods in a rigorous, yet intuitive way, without an excess of mathematical details. In this fifth edition, all chapters have been revised and updated, with clearer and more direct language than in previous editions, and with more up-to-date examples, exercises and references, in areas as diverse as biology, environmental sciences, economics, social medicine, and politics.
Features
- A concise and accessible conceptual approach that requires minimal mathematical background.
- Suitable for a wide range of applied statisticians and professionals from the natural and social sciences.
- Presents all the key topics for a multivariate statistics course.
- The R code in the appendices has been updated, and there is a new appendix introducing programming basics for R.
- The data from examples and exercises are available on a companion website.
This book continues to be a great starting point for readers looking to become proficient in multivariate statistical methods, but who might not be deeply versed in the language of mathematics. In this edition, we provide readers with conceptual introductions to methods, practical suggestions, new references, and a more extensive collection of R functions and code that will help them to deepen their toolkit of multivariate statistical methods.
Product Details
ISBN-13: | 9781032592008 |
---|---|
Publisher: | CRC Press |
Publication date: | 10/04/2024 |
Edition description: | 5th ed. |
Pages: | 288 |
Product dimensions: | 6.12(w) x 9.19(h) x (d) |
Table of Contents
Chapter 1 | The material of multivariate analysis | 1 |
1.1 | Examples of multivariate data | 1 |
1.2 | Preview of multivariate methods | 12 |
1.3 | The multivariate normal distribution | 14 |
1.4 | Computer programs | 15 |
1.5 | Graphical methods | 15 |
1.6 | Chapter summary | 16 |
References | 16 | |
Chapter 2 | Matrix algebra | 17 |
2.1 | The need for matrix algebra | 17 |
2.2 | Matrices and vectors | 17 |
2.3 | Operations on matrices | 19 |
2.4 | Matrix inversion | 21 |
2.5 | Quadratic forms | 22 |
2.6 | Eigenvalues and eigenvectors | 22 |
2.7 | Vectors of means and covariance matrices | 23 |
2.8 | Further reading | 25 |
2.9 | Chapter summary | 25 |
References | 26 | |
Chapter 3 | Displaying multivariate data | 27 |
3.1 | The problem of displaying many variables in two dimensions | 27 |
3.2 | Plotting index variables | 27 |
3.3 | The draftsman's plot | 29 |
3.4 | The representation of individual data points | 30 |
3.5 | Profiles of variables | 32 |
3.6 | Discussion and further reading | 33 |
3.7 | Chapter summary | 34 |
References | 34 | |
Chapter 4 | Tests of significance with multivariate data | 35 |
4.1 | Simultaneous tests on several variables | 35 |
4.2 | Comparison of mean values for two samples: the single variable case | 35 |
4.3 | Comparison of mean values for two samples: the multivariate case | 37 |
4.4 | Multivariate versus univariate tests | 41 |
4.5 | Comparison of variation for two samples: the single-variable case | 42 |
4.6 | Comparison of variation for two samples: the multivariate case | 42 |
4.7 | Comparison of means for several samples | 46 |
4.8 | Comparison of variation for several samples | 49 |
4.9 | Computer programs | 54 |
4.10 | Chapter summary | 54 |
Exercise | 55 | |
References | 57 | |
Chapter 5 | Measuring and testing multivariate distances | 59 |
5.1 | Multivariate distances | 59 |
5.2 | Distances between individual observations | 59 |
5.3 | Distances between populations and samples | 62 |
5.4 | Distances based on proportions | 67 |
5.5 | Presence-absence data | 68 |
5.6 | The Mantel randomization test | 69 |
5.7 | Computer programs | 72 |
5.8 | Discussion and further reading | 72 |
5.9 | Chapter summary | 73 |
Exercise | 74 | |
References | 74 | |
Chapter 6 | Principal components analysis | 75 |
6.1 | Definition of principal components | 75 |
6.2 | Procedure for a principal components analysis | 76 |
6.3 | Computer programs | 84 |
6.4 | Further reading | 85 |
6.5 | Chapter summary | 85 |
Exercises | 87 | |
References | 90 | |
Chapter 7 | Factor analysis | 91 |
7.1 | The factor analysis model | 91 |
7.2 | Procedure for a factor analysis | 93 |
7.3 | Principal components factor analysis | 95 |
7.4 | Using a factor analysis program to do principal components analysis | 97 |
7.5 | Options in analyses | 100 |
7.6 | The value of factor analysis | 101 |
7.7 | Computer programs | 101 |
7.8 | Discussion and further reading | 102 |
7.9 | Chapter summary | 102 |
Exercise | 103 | |
References | 103 | |
Chapter 8 | Discriminant function analysis | 105 |
8.1 | The problem of separating groups | 105 |
8.2 | Discrimination using Mahalanobis distances | 105 |
8.3 | Canonical discriminant functions | 107 |
8.4 | Tests of significance | 108 |
8.5 | Assumptions | 109 |
8.6 | Allowing for prior probabilities of group membership | 114 |
8.7 | Stepwise discriminant function analysis | 114 |
8.8 | Jackknife classification of individuals | 116 |
8.9 | Assigning of ungrouped individuals to groups | 116 |
8.10 | Logistic regression | 117 |
8.11 | Computer programs | 122 |
8.12 | Discussion and further reading | 122 |
8.13 | Chapter summary | 123 |
Exercises | 124 | |
References | 124 | |
Chapter 9 | Cluster analysis | 125 |
9.1 | Uses of cluster analysis | 125 |
9.2 | Types of cluster analysis | 125 |
9.3 | Hierarchic methods | 127 |
9.4 | Problems of cluster analysis | 129 |
9.5 | Measures of distance | 129 |
9.6 | Principal components analysis with cluster analysis | 130 |
9.7 | Computer programs | 134 |
9.8 | Discussion and further reading | 135 |
9.9 | Chapter summary | 136 |
Exercises | 137 | |
References | 141 | |
Chapter 10 | Canonical correlation analysis | 143 |
10.1 | Generalizing a multiple regression analysis | 143 |
10.2 | Procedure for a canonical correlation analysis | 145 |
10.3 | Tests of significance | 146 |
10.4 | Interpreting canonical variates | 148 |
10.5 | Computer programs | 158 |
10.6 | Further reading | 158 |
10.7 | Chapter summary | 159 |
Exercise | 159 | |
References | 161 | |
Chapter 11 | Multidimensional scaling | 163 |
11.1 | Constructing a map from a distance matrix | 163 |
11.2 | Procedure for multidimensional scaling | 165 |
11.3 | Computer programs | 172 |
11.4 | Further reading | 174 |
11.5 | Chapter summary | 174 |
Exercise | 175 | |
References | 175 | |
Chapter 12 | Ordination | 177 |
12.1 | The ordination problem | 177 |
12.2 | Principal components analysis | 178 |
12.3 | Principal coordinates analysis | 181 |
12.4 | Multidimensional scaling | 189 |
12.5 | Correspondence analysis | 191 |
12.6 | Comparison of ordination methods | 196 |
12.7 | Computer programs | 197 |
12.8 | Further reading | 197 |
12.9 | Chapter summary | 198 |
Exercise | 198 | |
References | 198 | |
Chapter 13 | Epilogue | 201 |
13.1 | The next step | 201 |
13.2 | Some general reminders | 201 |
13.3 | Missing values | 202 |
References | 203 | |
Appendix | Computer packages for multivariate analyses | 205 |
References | 207 | |
Author Index | 209 | |
Subject Index | 211 |