This accessible book has established itself as the goto resource on confirmatory factor analysis (CFA) for its emphasis on practical and conceptual aspects rather than mathematics or formulas. Detailed, workedthrough examples drawn from psychology, management, and sociology studies illustrate the procedures, pitfalls, and extensions of CFA methodology. The text shows how to formulate, program, and interpret CFA models using popular latent variable software packages (LISREL, Mplus, EQS, SAS/CALIS); understand the similarities and differences between CFA and exploratory factor analysis (EFA); and report results from a CFA study. It is filled with useful advice and tables that outline the procedures. The companion website offers data and program syntax files for most of the research examples, as well as links to CFArelated resources.
New to This Edition
*Updated throughout to incorporate important developments in latent variable modeling.
*Chapter on Bayesian CFA and multilevel measurement models.
*Addresses new topics (with examples): exploratory structural equation modeling, bifactor analysis, measurement invariance evaluation with categorical indicators, and a new method for scaling latent variables.
*Utilizes the latest versions of major latent variable software packages.
“Brown's writing is excellent; this book does a clearer and better job of explaining CFA concepts than any other I have read. It has had a very positive impact on the quality of applied CFA studies in the social and behavioral sciences. I will continue to use the second edition in my graduate measurement theory course; it enables my students to greatly improve the quality of their dissertation research. This is the best book I've seen for providing graduate students with the skills they need to develop and evaluate measures of psychological constructs."—G. Leonard Burns, PhD, Department of Psychology, Washington State University
“I am a big fan of this book. When something goes wrong in SEM, it is almost always due to a faulty measurement model, so students need to have a thorough understanding of latent trait measurement models before learning how to evaluate structural models. That is why this book is so important. My students regularly comment on how accessible the text is. I very much like the examples of study results, which students can use as templates for their own reports. The numerically worked examples throughout are extremely helpful at demystifying the process.”—Lesa Hoffman, PhD, Institute for Lifespan Studies, University of Kansas
“This book occupies a unique and important position in the field. It describes the use of CFA to address a wide range of important social science research questions that are too often ignored or underdeveloped in books on structural equation modeling. The text helps readers understand the nuances of CFA in a way that is deep yet incredibly accessible. I highly recommend this book to students and experienced social scientists interested in applying this powerful approach in their research.”—Noel A. Card, PhD, Department of Educational Psychology, University of Connecticut
“The most comprehensive reference text on CFA for experienced researchers. Other texts typically devote a chapter or two to the subject, but Brown’s coverage is wide and deep. Frankly, what gives this book value to me is that it is a reference text that can be used for instruction. Aided by clear examples, simplified tables, and helpful visual depictions, readers easily gain an understanding of how to run popular modeling software and correctly interpret the output. Perhaps one of the finest jewels in this book is the explanation of nonpositive definite matrices, the bane of LISREL users. I also find the thread throughout the book on explaining equivalent models very important.”—Randall MacIntosh, PhD, Professor of Sociology, California State University, Sacramento
“I highly recommend this book to colleagues and students who teach and apply structural equation modeling. The book provides an invaluable resource for applied researchers concerning concepts, procedures, and problems in CFA, as well as how to interpret and report analysis results. An especially valuable feature is the many detailed examples that are worked out in detail and presented along with syntax and output from leading software packages. The Appendices at the end of several chapters expand on many technical points the reader might fail to grasp otherwise.”—James G. Anderson, PhD, Department of Sociology, Purdue University
“The book does an excellent job of walking through the steps in an analysis. It is wonderfully user friendly in the way it presents each step, discusses major decisions to be made, and presents some code and output. Not only do I think this is the best book out there for learning CFA, but I also think it is a fantastic way to learn introductory structural equation modeling methods.”—Scott J. Peters, PhD, Department of Educational Foundations, University of Wisconsin–Whitewater
“A strength of this book is the style of the author's presentation. Many important concepts are explained in plain language, rather than by mathematical formula. The book reads as though you were listening to a lecture. It provides the learner with an extensive understanding of the theory and applications of CFA. I also strongly recommend this book to practitioners who are in need of a comprehensive reference for better applications of CFA."—Akihito Kamata, PhD, Department of Education Policy and Leadership and Department of Psychology, Southern Methodist University
*The first (and still only) complete resource on using CFA as an analytic tool, revised and expanded: 25% new material addresses the latest developments in the field.
*Popular with researchers and students for its emphasis on the practical aspects of CFA over math and formulas.
*Rich examples are derived from actual research in psychology, management, and sociology.
*Covers all popular software packages (LISREL, Mplus, EQS, SAS PROC CALIS, and more), plus advanced topics.
*From a topselling textbook author who presents internationally, most recently in the UK, the Netherlands, and Germany.
*Online supplement includes datasets from the examples and links to related resources.
Applied researchers in psychology, education, management/marketing, sociology, public health, and other behavioral and social sciences; graduatelevel students.
Serves as a core or supplemental text in courses on factor analysis, structural equation modeling, advanced statistics, psychometrics, latent trait measurement models, or scale development.
Uses of Confirmatory Factor Analysis
Psychometric Evaluation of Test Instruments
Measurement Invariance Evaluation
Why a Book on CFA?
Coverage of the Book
2. The Common Factor Model and Exploratory Factor Analysis
Overview of the Common Factor Model
Procedures of EFA
3. Introduction to CFA
Similarities and Differences of EFA and CFA
Common Factor Model
Standardized and Unstandardized Solutions
Indicator Cross-Loadings/Model Parsimony
Purposes and Advantages of CFA
Parameters of a CFA Model
Fundamental Equations of a CFA Model
CFA Model Identification
Scaling the Latent Variable
Guidelines for Model Identification
Estimation of CFA Model Parameters
Descriptive Goodness-of-Fit Indices
Guidelines for Interpreting Goodness-of-Fit Indices
Appendix 3.1. Communalities, Model-Implied Correlations, and
Factor Correlations in EFA and CFA
Appendix 3.2. Obtaining a Solution for a Just-Identified Factor Model
Appendix 3.3. Hand Calculation of FML for the Figure 3.8 Path Model
4. Specification and Interpretation of CFA Models
An Applied Example of a CFA Measurement Model
Defining the Metric of Latent Variables
Data Screening and Selection of the Fitting Function
Running CFA in Different Software Programs
Overall Goodness of Fit
Localized Areas of Strain
Interpretability, Size, and Statistical Significance of the Parameter
Interpretation and Calculation of CFA Model Parameter Estimates
CFA Models with Single Indicators
Reporting a CFA Study
Appendix 4.1. Model Identification Affects the Standard Errors of the
Appendix 4.2. Goodness of Model Fit Does Not Ensure Meaningful
Appendix 4.3. Example Report of the Two-Factor CFA Model of Neuroticism
5. Model Revision and Comparison
Goals of Model Respecification
Sources of Poor-Fitting CFA Solutions
Number of Factors
Indicators and Factor Loadings
Improper Solutions and Nonpositive Definite Matrices
Intermediate Steps for Further Developing a Measurement Model for CFA
EFA in the CFA Framework
Model Identification Revisited
Equivalent CFA Solutions
6. CFA of Multitrait–Multimethod Matrices
Correlated versus Random Measurement Error Revisited
The Multitrait–Multimethod Matrix
CFA Approaches to Analyzing the MTMM Matrix
Correlated Methods Models
Correlated Uniqueness Models
Advantages and Disadvantages of Correlated Methods and Correlated
Other CFA Parameterizations of MTMM Data
Consequences of Not Modeling Method Variance and Measurement Error
7. CFA with Equality Constraints, Multiple Groups, and Mean Structures
Overview of Equality Constraints
Equality Constraints within a Single Group
Congeneric, Tau-Equivalent, and Parallel Indicators
Longitudinal Measurement Invariance
The Effects Coding Approach to Scaling Latent Variables
CFA in Multiple Groups
Overview of Multiple-Groups Solutions
Selected Issues in Single- and Multiple-Groups CFA Invariance
MIMIC Modeling (CFA with Covariates)
Appendix 7.1. Reproduction of the Observed Variance–Covariance Matrix with
Tau-Equivalent Indicators of Auditory Memory
8. Other Types of CFA Models: Higher-Order Factor Analysis, Scale Reliability
Evaluation, and Formative Indicators
Higher-Order Factor Analysis
Second-Order Factor Analysis
Scale Reliability Estimation
Point Estimation of Scale Reliability
Standard Error and Interval Estimation of Scale Reliability
Models with Formative Indicators
9. Data Issues in CFA: Missing, Non-Normal, and Categorical Data
CFA with Missing Data
Mechanisms of Missing Data
Conventional Approaches to Missing Data
Recommended Strategies for Missing Data
CFA with Non-Normal or Categorical Data
Non-Normal, Continuous Data
Other Potential Remedies for Indicator Non-Normality
10. Statistical Power and Sample Size
Monte Carlo Approach
Appendix 10.1. Monte Carlo Simulation in Greater Depth: Data Generation
11. Recent Developments Involving CFA Models
Bayesian Probability and Statistical Inference
Priors in CFA
Applied Example of Bayesian CFA
Bayesian CFA: Summary
Appendix 11.1. Numerical Example of Bayesian Probability
About the Author
ABOUT THE AUTHOR
Timothy A. Brown, PsyD, is Professor in the Department of Psychology and Director of Research at the Center for Anxiety and Related Disorders at Boston University. He has published extensively in the areas of the classification of anxiety and mood disorders, the psychopathology and risk factors of emotional disorders, psychometrics, and applied research methods. In addition to conducting his own grantsupported research, Dr. Brown serves as a statistical investigator or consultant on numerous federally funded research projects. He has been on the editorial boards of several scientific journals, including a longstanding appointment as Associate Editor of the Journal of Abnormal Psychology.