# Contents

## Setting the scene

• Structure of the book
• Our limited use of mathematics
• Variables
• The geometry of multivariate analysis
• Use of examples
• Data inspection, transformations, and missing data

## Cluster analysis

• Classification in social sciences
• Some methods of cluster analysis
• Graphical presentation of results
• Derivation of the distance matrix
• Example on English dialects
• Comparisons
• Clustering variables
• Additional examples and further work

## Multidimensional scaling

• Sample chapter: multidimensional scaling
• Introduction
• Examples
• Classical, ordinal, and metrical multidimensional scaling
• Assessing fit and choosing the number of dimensions
• A worked example: dimensions of colour vision
• Additional examples and further work

## Correspondence analysis

• Aims of correspondence analysis
• Carrying out a correspondence analysis: a simple numerical example
• Carrying out a correspondence analysis: the general method
• The biplot Interpretation of dimensions
• Choosing the number of dimensions
• Example: confidence in purchasing from European Community countries correspondence analysis of multiway tables
• Additional examples and further work

## Principal components analysis

• Introduction
• Some potential applications
• Illustration of PCA for two variables
• An outline of PCA
• Examples
• Component scores
• The link between PCA and multidimensional scaling and between PCA and correspondence analysis
• Using principal component scores to replace the original variables
• Additional examples and further work

## Regression analysis

• Basic ideas
• Simple linear regression
• A probability model for simple linear regression
• Inference for the simple linear regression model
• Checking the assumptions
• Multiple regression
• Examples of multiple regression
• Estimation and inference about the parameters
• Interpretation of the regression coefficients
• Selection of regressor variables
• Transformations and interactions
• Logistic regression
• Path analysis
• Additional examples and further work

## Factor analysis

• Introduction to latent variable models
• The linear single-factor model
• The general linear factor model
• Interpretation
• Adequacy of the model and choice of the number of factors
• Rotation
• Factor scores
• A worked example: the test anxiety inventory
• How rotation helps interpretation
• A comparison of factor analysis and principal components analysis
• Additional examples and further work
• Software

## Factor analysis for binary data

• Sample chapter: Factor Analysis for Binary Data
• Latent trait models
• Why is the factor analysis model for metrical variables invalid for binary responses?
• Factor model for binary data using the item response theory approach
• Goodness-of-fit
• Factor scores
• Rotation
• Underlying variable approach
• Example: sexual attitudes
• Additional examples and further work
• Software

## Factor analysis for ordered categorical variables

• The practical background
• Two approaches to modeling ordered categorical data
• Item response function approach
• Examples
• The underlying variable approach
• Unordered and partially ordered observed variables
• Additional examples and further work
• Software

## Latent class analysis for binary data

• Introduction
• The latent class model for binary data
• Example: attitude to science and technology data
• How can we distinguish the latent class model from the latent trait model?
• Latent class analysis, cluster analysis, and latent profile analysis
• Additional examples and further work
• Software

## Confirmatory factor analysis and structural equation models

• Introduction
• Path diagram
• Measurement models
• Introduction to structural equation models with latent variables
• The linear structural equation model
• A worked example
• Extensions
• Software

## Multilevel modelling

• Introduction
• Some potential applications
• Comparing groups using multilevel modelling
• Random intercept model
• Random slope model
• Contextual effects
• Multilevel multivariate regression
• Multilevel factor analysis
• Additional examples and further work
• Further topics
• Estimation procedures and software

## References

Index

Further reading sections appear at the end of each chapter.