Applied Multivariate Data Analysis

by Brian S. Everitt; Graham Dunn

• ISBN13: 9780340741221
• ISBN10: 0340741228
• Edition: 2nd
• Format: Paperback
• Copyright: 2001-05-03
• Publisher: Hodder Education Publishers

Summary

This book is fully updated to include new sections on neural networks, graphical modelling, hierarchical or multilevel modelling, and latent class models. The sections on correspondence analysis and principal components analysis have been expanded. It also offers more exercises for students and an updated review of the available software suited to multivariate analysis. The text avoids irrelevant theoretical statistics and concentrates on enabling the students to understand the concepts behind the data analysis.

Author Biography

Brian S. Everitt is Professor of Behavioural Statistics and Head of the Biostatistics and Computing Department at the Institute of Psychiatry, King's College London, UK.

Table of Contents

Multivariate data and multivariate statistics	1	(8)
Introduction	1	(1)
Types of data	2	(2)
Basic multivariate statistics	4	(2)
The aims of multivariate analysis	6	(3)
Exploring multivariate data graphically	9	(39)
Introduction	9	(1)
The scatterplot	9	(6)
The scatterplot matrix	15	(2)
Enhancing the scatterplot	17	(9)
Coplots and trellis graphics	26	(15)
Checking distributional assumptions using probability plots	41	(4)
Summary	45	(3)
Exercises	45	(3)
Principal components analysis	48	(26)
Introduction	48	(1)
Algebraic basics of principal components	49	(3)
Rescaling principal components	52	(1)
Calculating principal component scores	53	(1)
Choosing the number of components	53	(1)
Two simple examples of principal components analysis	54	(2)
More complex examples of the application of principal components analysis	56	(7)
Using principal components analysis to select a subset of variables	63	(2)
Using the last few principal components	65	(1)
The biplot	65	(4)
Geometrical interpretation of principal components analysis	69	(1)
Projection pursuit	69	(2)
Summary	71	(3)
Exercises	71	(3)
Correspondence analysis	74	(19)
Introduction	74	(1)
A simple example of correspondence analysis	75	(3)
Correspondence analysis for two-dimensional contingency tables	78	(2)
Three applications of correspondence analysis	80	(4)
Multiple correspondence analysis	84	(7)
Summary	91	(2)
Exercises	91	(2)
Multidimensional scaling	93	(32)
Introduction	93	(1)
Proximity matrices and examples of multidimensional scaling	94	(10)
Metric least-squares multidimensional scaling	104	(3)
Non-metric multidimensional scaling	107	(6)
Non-Euclidean metrics	113	(1)
Three-way multidimensional scaling	114	(5)
Inference in multidimensional scaling	119	(3)
Summary	122	(3)
Exercises	122	(3)
Cluster analysis	125	(36)
Introduction	125	(3)
Agglomerative hierarchical clustering techniques	128	(14)
Optimization methods	142	(6)
Finite mixture models for cluster analysis	148	(10)
Summary	158	(3)
Exercises	158	(3)
The generalized linear model	161	(12)
Linear models	161	(4)
Non-linear models	165	(3)
Link functions and error distributions in the generalized linear model	168	(3)
Summary	171	(2)
Exercises	172	(1)
Regression and the analysis of variance	173	(25)
Introduction	173	(1)
Least-squares estimation for regression and analysis of variance models	173	(17)
Direct and indirect effects	190	(5)
Summary	195	(3)
Exercises	195	(3)
Log-linear and logistic models for categorical multivariate data	198	(20)
Introduction	198	(1)
Maximum likelihood estimation for log-linear and linear-logistic models	199	(13)
Transition models for repeated binary response measures	212	(4)
Summary	216	(2)
Exercises	216	(2)
Models for multivariate response variables	218	(30)
Introduction	218	(1)
Repeated quantitative measures	218	(4)
Multivariate tests	222	(2)
Random effects models for longitudinal data	224	(13)
Logistic models for multivariate binary responses	237	(3)
Marginal models for repeated binary response measures	240	(2)
Marginal modelling using generalized estimating equations	242	(2)
Random effects models for multivariate repeated binary response measures	244	(2)
Summary	246	(2)
Exercises	246	(2)
Discrimination, classification and pattern recognition	248	(23)
Introduction	248	(1)
A simple example	249	(1)
Some examples of allocation rules	250	(3)
Fisher's linear discriminant function	253	(1)
Assessing the performance of a discriminant function	254	(1)
Quadratic discriminant functions	255	(2)
More than two groups	257	(3)
Logistic discrimination	260	(2)
Selecting variables	262	(1)
Other methods for deriving classification rules	263	(1)
Pattern recognition and neural networks	264	(4)
Summary	268	(3)
Exercises	268	(3)
Exploratory factor analysis	271	(20)
Introduction	271	(1)
The basic factor analysis model	272	(2)
Estimating the parameters in the factor analysis model	274	(4)
Rotation of factors	278	(2)
Some examples of the application of factor analysis	280	(3)
Estimating factor scores	283	(1)
Factor analysis with categorical variables	284	(3)
Factor analysis and principal components analysis compared	287	(1)
Summary	287	(4)
Exercises	288	(3)
Confirmatory factor analysis and covariance structure models	291	(33)
Introduction	291	(1)
Path analysis and path diagrams	292	(3)
Estimation of the parameters in structural equation models	295	(1)
A simple covariance structure model and identification	295	(2)
Assessing the fit of a model	297	(1)
Some examples of fitting confirmatory factor analysis models	298	(4)
Structural equation models	302	(2)
Causal models and latent variables: myths and realities	304	(2)
Summary	306	(2)
Exercises	306	(2)
Appendices
A Software packages	308	(3)
A.1 General-purpose packages	308	(1)
A.2 More specialized packages	309	(2)
B Missing Values	311	(3)
C Answers to selected exercises	314	(10)
References	324	(13)
Index	337