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| Preface | |
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| Setting the Scene | |
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| Structure of the book | |
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| Our limited use of mathematics | |
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| Variables | |
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| The geometry of multivariate analysis | |
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| Use of examples | |
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| Data inspection, transformations, and missing data | |
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| Reading | |
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| Cluster Analysis | |
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| Classification in social sciences | |
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| Some methods of cluster analysis | |
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| Graphical presentation of results | |
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| Derivation of the distance matrix | |
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| Example on English dialects | |
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| Comparisons | |
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| Clustering variables | |
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| Additional examples and further work | |
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| Further reading | |
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| Multidimensional Scaling | |
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| Introduction | |
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| Examples | |
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| Classical, ordinal, and metrical multidimensional scaling | |
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| Comments on computational procedures | |
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| Assessing fit and choosing the number of dimensions | |
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| A worked example: dimensions of colour vision | |
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| Additional examples and further work | |
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| Further reading | |
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| Correspondence Analysis | |
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| Aims of correspondence analysis | |
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| Carrying out a correspondence analysis: a simple numerical example | |
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| Carrying out a correspondence analysis: the general method | |
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| The biplot | |
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| Interpretation of dimensions | |
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| Choosing the number of dimensions | |
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| Example: confidence in purchasing from European Community countries | |
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| Correspondence analysis of multiway tables | |
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| Additional examples and further work | |
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| Further reading | |
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| Principal Components Analysis | |
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| Introduction | |
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| Some potential applications | |
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| Illustration of PCA for two variables | |
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| An outline of PCA | |
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| Examples | |
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| Component scores | |
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| The link between PCA and multidimensional scaling, and between PCA and correspondence analysis | |
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| Using principal component scores to replace the original variables | |
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| Additional examples and further work | |
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| Further reading | |
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| Regression Analysis | |
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| Basic ideas | |
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| Simple linear regression | |
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| A probability model for simple linear regression | |
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| Inference for the simple linear regression model | |
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| Checking the assumptions | |
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| Multiple regression | |
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| Examples of multiple regression | |
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| Estimation and inference about the parameters | |
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| Interpretation of the regression coefficients | |
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| Selection of regressor variables | |
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| Transformations and interactions | |
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| Logistic regression | |
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| Path analysis | |
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| Additional examples and further work | |
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| Further reading | |
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| Factor Analysis | |
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| Introduction to latent variable models | |
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| The linear single-factor model | |
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| The general linear factor model | |
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| Interpretation | |
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| Adequacy of the model and choice of the number of factors | |
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| Rotation | |
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| Factor scores | |
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| A worked example: the test anxiety inventory | |
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| How rotation helps interpretation | |
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| A comparison of factor analysis and principal components analysis | |
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| Additional examples and further work | |
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| Software | |
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| Further reading | |
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| Factor Analysis for Binary Data | |
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| Latent trait models | |
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| Why is the factor analysis model for metrical variables invalid for binary responses? | |
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| Factor model for binary data using the Item Response Theory approach | |
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| Goodness-of-fit | |
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| Factor scores | |
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| Rotation | |
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| Underlying variable approach | |
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| Example: sexual attitudes | |
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| Additional examples and further work | |
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| Software | |
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| Further reading | |
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| Factor Analysis for Ordered Categorical Variables | |
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| The practical background | |
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| Two approaches to modelling ordered categorical data | |
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| Item response function approach | |
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| Examples | |
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| The underlying variable approach | |
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| Unordered and partially ordered observed variables | |
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| Additional examples and further work | |
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| Software | |
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| Further reading | |
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| Latent Class Analysis for Binary Data | |
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| Introduction | |
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| The latent class model for binary data | |
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| Example: attitude to science and technology data | |
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| How can we distinguish the latent class model from the latent trait model? | |
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| Latent class analysis, cluster analysis, and latent profile analysis | |
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| Additional examples and further work | |
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| Software | |
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| Further reading | |
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| Confirmatory Factor Analysis and Structural Equation Models | |
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| Introduction | |
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| Path diagram | |
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| Measurement models | |
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| Adequacy of the model | |
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| Introduction to structural equation models with latent variables | |
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| The linear structural equation model | |
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| A worked example | |
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| Extensions | |
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| Additional examples and further work | |
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| Software | |
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| Further reading | |
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| Multilevel Modelling | |
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| Introduction | |
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| Some potential applications | |
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| Comparing groups using multilevel modelling | |
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| Random intercept model | |
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| Random slope model | |
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| Contextual effects | |
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| Multilevel multivariate regression | |
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| Multilevel factor analysis | |
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| Additional examples and further work | |
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| Further topics | |
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| Estimation procedures and software | |
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| Further reading | |
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| References | |
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| Index | |