Applied Multivariate Data Analysis, 2nd Edition

1.1 Introduction.

1.2 Types of data.

1.3 Basic multivariate statistics.

1.4 The aims of multivariate analysis.

2 Exploring multivariate data graphically.

2.1 Introduction.

2.2 The scatterplot.

2.3 The scatterplot matrix.

2.4 Enhancing the scatterplot.

2.5 Coplots and trellis graphics.

2.6 Checking distributional assumptions using probability plots.

2.7 Summary.

Exercises.

3 Principal components analysis.

3.1 Introduction.

3.2 Algebraic basics of principal components.

3.3 Rescaling principal components.

3.4 Calculating principal component scores.

3.5 Choosing the number of components.

3.6 Two simple examples of principal components analysis.

3.7 More complex examples of the application of principal components analysis.

3.8 Using principal components analysis to select a subset of variables.

3.9 Using the last few principal components.

3.10 The biplot.

3.11 Geometrical interpretation of principal components analysis.

3.12 Projection pursuit.

3.13 Summary.

Exercises.

4 Correspondence analysis.

4.1 Introduction.

4.2 A simple example of correspondence analysis.

4.3 Correspondence analysis for two-dimensional contingency tables.

4.4 Three applications of correspondence analysis.

4.5 Multiple correspondence analysis.

4.6 Summary

Exercises.

5 Multidimensional scaling.

5.1 Introduction.

5.2 Proximity matrices and examples of multidimensional scaling.

5.4 Metric least-squares multidimensional scaling.

5.5 Non-metric multidimensional scaling.

5.6 Non-Euclidean metrics.

5.7 Three-way multidimensional scaling.

5.8 Inference in multidimensional scaling.

5.9 Summary.

Exercises.

6 Cluster analysis.

6.1 Introduction.

6.2 Agglomerative hierarchical clustering techniques.

6.3 Optimization methods.

6.4 Finite mixture models for cluster analysis.

6.5 Summary.

Exercises.

7 The generalized linear model.

7.1 Linear models.

7.2 Non-linear models.

7.3 Link functions and error distributions in the generalized linear model.

7.4 Summary.

Exercises.

8 Regression and the analysis of variance.

8.1 Introduction.

8.2 Least-squares estimation for regression and analysis of variance models.

8.3 Direct and indirect effects.

8.4 Summary.

Exercises.

9 Log-linear and logistic models for categorical multivariate data.

9.1 Introduction.

9.2 Maximum likelihood estimation for log-linear and linear-logistic models.

9.3 Transition models for repeated binary response measures.

9.4 Summary.

Exercises.

10 Models for multivariate response variables.

10.1 Introduction.

10.2 Repeated quantitative measures.

10.3 Multivariate tests.

10.4 Random effects models for longitudinal data.

10.5 Logistic models for multivariate binary responses.

10.6 Marginal models for repeated binary response measures.

10.7 Marginal modelling using generalized estimating equations.

10.8 Random effects models for multivariate repeated binary response measures.

10.9 Summary.

Exercises.

11 Discrimination, classification and pattern recognition.

11.1 Introduction.

11.2 A simple example.

11.3 Some examples of allocation rules.

11.4 Fisher's linear discriminant function.

11.5 Assessing the performance of a discriminant function.

11.6 Quadratic discriminant functions.

11.7 More than two groups.

11.8 Logistic discrimination.

11.9 Selecting variables.

11.10 Other methods for deriving classification rules.

11.11 Pattern recognition and neural networks.

11.12 Summary.

Exercises.

12 Exploratory factor analysis.

12.1 Introduction.

12.2 The basic factor analysis model.

12.3 Estimating the parameters in the factor analysis model.

12.4 Rotation of factors.

12.5 Some examples of the application of factor analysis.

12.6 Estimating factor scores.

12.7 Factor analysis with categorical variables.

12.8 Factor analysis and principal components analysis compared.

12.9 Summary.

Exercises.

13 Confirmatory factor analysis and covariance structure models.

13.1 Introduction.

13.2 Path analysis and path diagrams.

13.3 Estimation of the parameters in structural equation models.

13.4 A simple covariance structure model and identification.

13.5 Assessing the fit of a model.

13.6 Some examples of fitting confirmatory factor analysis models.

13.7 Structural equation models.

13.8 Causal models and latent variables: myths and realities.

13.9 Summary.

Exercises.

Appendices.

A Software packages.

A.1 General-purpose packages.

A.2 More specialized packages.

B Missing values.

C Answers to selected exercises.

References.

Index.