Multivariate Statistical Methods: A Primer

by Bryan F. J. Manly, Jorge A. Navarro Alberto, Ken Gerow

Overview

For those looking to become proficient in multivariate statistical methods, but who might not be deeply versed in the language of mathematics, provides conceptual intros to methods, practical suggestions, new references, and a more extensive collection of R functions and code that will deepen toolkit of multivariate statistical methods.

Product Details

ISBN-13:	9781032591971
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)

About the Author

Bryan Manly, PhD, was born in London, UK on May 27, 1944, and he is practically retired from academic work. His areas of interest are in statistical ecology, environmental statistics, computer intensive statistics, and general applied statistics. He is the author of over two hundred papers and seven books that have been both fundamental statistical research, and applications to several related disciplines. Bryan's academic career began in 1966 as a statistician and one of the first computer programmers, at the British multinational manufacturer Fisons, marking the start of a brilliant career as a researcher and statistical consultant in several countries around the world: University of Salford (UK), University of Papua New Guinea, University of Otago (New Zealand), Louisiana State University, University of Wyoming, and WEST, Inc. (USA). Among other distinctions, he is an Elected Fellow of the Royal Society of New Zealand, and he was awarded as Distinguished Statistical Ecologist in the International Ecology Congress, held in Manchester, 1994. Bryan is an excellent connoisseur of home brewing and homemade wine; everybody praises his good hand in making peerless wine!

Jorge A. Navarro Alberto, PhD, is a professor emeritus at the Autonomous University of Yucatán, México, where he specialized in ecological and environmental statistics research. Dr. Navarro Alberto earned his PhD degree in Statistics at the University of Otago, New Zealand. His academic career spanned more than 36 years teaching statistics for biologists, marine biologists, and natural resource managers in Mexico, and as a visiting professor at the University of Wyoming, with a vast experience in teaching multivariate analysis courses for life scientists. He is the co-author of the last edition of the book Randomization, Bootstrap and Monte Carlo Methods in Biology, and the co-editor of Introduction to Ecological Sampling, published by CRC Press. After retirement, Jorge is still active in the professional and academic arenas, working as a (more relaxed) part-time statistical consultant, and as one of the associate editors of the international journal, Environmental and Ecological Statistics. He also member of the Mexican representation at the International Statistical Literacy Project, Finland.

Ken Gerow, PhD, recently retired from the University of Wyoming, where, as a professor of statistics for over thirty years, he taught statistics to quantitative scientists from many disciplines. Dr. Gerow earned his PhD degree in Statistics at Cornell University. He is the author or a coauthor of over ninety research articles, books, and book chapters, in topics ranging from the molecular and cellular world to the visible world around us (plant, animal, and human systems). Ken considers himself to be a parasitic biologist because he only publishes with other people's data.

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

Editorial Reviews

An introduction for nonmathematicians who have previously taken a standard introductory course of statistical methods. The first five chapters deal with general aspects of multivariate data, such as tests of significance and measuring and testing multivariate distances. The rest of the book covers multivariate methods in terms of current use, including factor analysis, cluster analysis, and multidimensional scaling. This second edition contains new material on ordination, logistic regression, and ordination, plus exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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