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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 | |