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