2nd Edition

# Analysis of Multivariate Social Science Data

**Also available as eBook on:**

Drawing on the authors’ varied experiences working and teaching in the field, **Analysis of Multivariate Social Science Data**,** Second Edition**enables a basic understanding of how to use key multivariate methods in the social sciences. With updates in every chapter, this edition expands its topics to include regression analysis, confirmatory factor analysis, structural equation models, and multilevel models.

After emphasizing the summarization of data in the first several chapters, the authors focus on regression analysis. This chapter provides a link between the two halves of the book, signaling the move from descriptive to inferential methods and from interdependence to dependence. The remainder of the text deals with model-based methods that primarily make inferences about processes that generate data.

Relying heavily on numerical examples, the authors provide insight into the purpose and working of the methods as well as the interpretation of data. Many of the same examples are used throughout to illustrate connections between the methods. In most chapters, the authors present suggestions for further work that go beyond conventional exercises, encouraging readers to explore new ground in social science research.

Requiring minimal mathematical and statistical knowledge, this book shows how various multivariate methods reveal different aspects of data and thus help answer substantive research questions.

**Preface**

**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

Further examples and suggestions for further work

**Multidimensional Scaling**

Introduction

Examples

Classical, ordinal, and metrical multidimensional scaling

Comments on computational procedures

Assessing fit and choosing the number of dimensions

A worked example: dimensions of color vision

Further examples and suggestions for 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

Further examples and suggestions for 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

Further examples and suggestions for further work

*NEW!***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

Further examples and suggestions for 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

Further examples and suggestions for further work

Software

**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

Further examples and suggestions for 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

Further examples and suggestions for 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

Further examples and suggestions for further work

Software

*NEW!***Confirmatory Factor Analysis and Structural Equation Models**

Introduction

Path diagram

Measurement models

Adequacy of the model

Introduction to structural equation models with latent variables

The linear structural equation model

A worked example

Extensions

Further examples

Software

*NEW!***Multilevel Modeling**

Introduction

Some potential applications

Comparing groups using multilevel modeling

Random intercept model

Random slope model

Contextual effects

Multilevel multivariate regression

Multilevel factor analysis

Further examples and suggestions for further work

Further topics

Estimation procedures and software

**References**

**Index**

*Further reading sections appear at the end of each chapter.*

### Biography

David J. Bartholomew, Fiona Steele, Fiona Steele, Irini Moustaki

"… Written by some of the leaders in the field, the second edition expands the horizon of the first edition by three new chapters. The new edition enabled the authors to deal with two equally important types of methods—those for data summarization and those that are model based. … The book should provide a superb introduction to these methods for graduate students who are without substantial statistical or mathematical training … Good examples abound [and] … so do worked-out applications. … I also like the authors’ effort to compare related methods across the chapters … The website is a treasure trove … the book is essential to read … ."

—Tim Futing Liao, University of Illinois,Journal of the Royal Statistical Society,Series A,2010"The strength of this book lies in the right mixture of simple mathematical expressions, comprehensive non-mathematical descriptions of various multivariate approaches, numerous interesting real-life data examples, and detailed interpretation of the results. … The comprehensive web resource the authors provide is also commendable. … Overall, this is an outstanding book on multivariate statistics in the field of social sciences, with a strong focus on categorical data. It can be recommended without reservations for quantitative graduate courses in psychology, sociology, education, and related areas. …"

—Journal of Statistical Software, February 2009"…I am pleased that the authors emphasise that the book is in no sense a cookbook. … the presentation is well matched to its intended audience, relying on only the minimal necessary mathematics and driving the development with examples, figures, and verbal descriptions. …This is the sort of book from which I would have liked to have learnt multivariate statistics."

—International Statistical Review, 2008