Applied Multivariate Data Analysis

Multivariate analysis plays an important role in the understanding of complex data sets requiring simultaneous examination of all variables. Breaking through the apparent disorder of the information, it provides the means for both describing and exploring data, aiming to extract the underlying patterns and structure. This intermediate-level textbook introduces the reader to the variety of methods by which multivariate statistical analysis may be undertaken. Now in its 2nd edition, 'Applied Multivariate Data Analysis' has been fully expanded and updated, including major chapter revisions as well as new sections on neural networks and random effects models for longitudinal data. Maintaining the easy-going style of the first edition, the authors provide clear explanations of each technique, as well as supporting figures and examples, and minimal technical jargon. With extensive exercises following every chapter, 'Applied Multivariate Data Analysis' is a valuable resource for students on applied statistics courses and applied researchers in many disciplines.

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

Graham Dunn is Professor of Biomedical Statistics and Head of the Biostatistics Group within the School of Epidemiology and Health Sciences, University of Manchester, UK

Multivariate data and multivariate statistics
Introduction
Types of data
Basic multivariate statistics
The aims of multivariate analysis
Exploring multivariate data graphically
Introduction
The scatterplot
The scatterplot matrix
Enhancing the scatterplot
Coplots and trellis graphics
Checking distributional assumptions using probability plots
Summary
Exercises
Principal components analysis
Introduction
Algebraic basics of principal components
Rescaling principal components
Calculating principal component scores
Choosing the number of components
Two simple examples of principal components analysis
More complex examples of the application of principal components analysis
Using principal components analysis to select a subset of variables
Using the last few principal components
The biplot
Geometrical interpretation of principal components analysis
Projection pursuit
Summary
Exercises
Correspondence analysis
Introduction
A simple example of correspondence analysis
Correspondence analysis for two-dimensional contingency tables
Three applications of correspondence analysis
Multiple correspondence analysis
Summary
Exercises
Multidimensional scaling
Introduction
Proximity matrices and examples of multidimensional scaling
Metric least-squares multidimensional scaling
Non-metric multidimensional scaling
Non-Euclidean metrics
Three-way multidimensional scaling
Inference in multidimensional scaling
Summary
Exercises
Cluster analysis
Introduction
Agglomerative hierarchical clustering techniques
Optimization methods
Finite mixture models for cluster analysis
Summary
Exercises
The generalized linear model
Linear models
Non-linear models
Link functions and error distributions in the generalized linear model
Summary
Exercises
Regression and the analysis of variance
Introduction
Least-squares estimation for regression and analysis of variance models
Direct and indirect effects
Summary
Exercises
Log-linear and logistic models for categorical multivariate data
Introduction
Maximum likelihood estimation for log-linear and linear-logistic models
Transition models for repeated binary response measures
Summary
Exercises
Models for multivariate response variables
Introduction
Repeated quantitative measures
Multivariate tests
Random effects models for longitudinal data
Logistic models for multivariate binary responses
Marginal models for repeated binary response measures
Marginal modelling using generalized estimating equations
Random effects models for multivariate repeated binary response measures
Summary
Exercises
Discrimination, classification and pattern recognition
Introduction
A simple example
Some examples of allocation rules
Fisher's linear discriminant function
Assessing the performance of a discriminant function
Quadratic discriminant functions
More than two groups
Logistic discrimination
Selecting variables
Other methods for deriving classification rules
Pattern recognition and neural networks
Summary
Exercises
Exploratory factor analysis
Introduction
The basic factor analysis model
Estimating the parameters in the factor analysis model
Rotation of factors
Some examples of the application of factor analysis
Estimating factor scores
Factor analysis with categorical variables
Factor analysis and principal components analysis compared
Summary
Exercises
Confirmatory factor analysis and covariance structure models
Introduction
Path analysis and path diagrams
Estimation of the parameters in structural equation models
A simple covariance structure model and identification
Assessing the fit of a model
Some examples of fitting confirmatory factor analysis models
Structural equation models
Causal models and latent variables: myths and realities
Summary
Exercises
Appendices
Software packages
General-purpose packages
More specialized packages
Missing values
Answers to selected exercises
References
Index
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Applied Multivariate Data Analysis

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