Synopses & Reviews
Review
"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 non-positive 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 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
Review
"I found the authors coverage of confirmatory factor analysis (CFA) both clear and accurate. I thought the explanations were pitched at the right level of mathematical and statistical complexity for the intended audience. In fact, the coverage of certain topics/m-/such as the problem of empirical under-identification and the computation of determinants and their functional significance in the assessment of global model fit/m-/is among the best Ive read. This is a book that students will be glad to have on their shelves when they turn to their own data later on."--Christopher M. Federico, Department of Psychology and Department of Political Science, University of Minnesota
"Compared to other books, this book offers a lot of details which would facilitate better understanding of confirmatory factor analysis (CFA). The author is very good at explaining a lot of processes by examples, and includes clear figures and tables. I definitely recommend it to instructors who teach a course on CFA, especially for students who are not in quantitative psychology."--Ke-Hai Yuan, Department of Psychology, University of Notre Dame
"I confidently recommend this book to any colleague teaching a course in confirmatory factor analysis (CFA), structural equation modeling, or scale development. The text will also be an invaluable resource for applied researchers, due to the quantity and quality of the information it contains. Included are very clear explanations of the 'thick' technical terminology and excellent elaboration on the shortcomings of the previously published CFA research within the past 10-15 years. Other strengths are clearly written chapters on higher order analyses and multitrait-multimethod models; clear coverage of conducting CFA with missing data and conducting reliability analysis within the general framework of SEM, providing a very defensible and unified approach to the issues of reliability and validity during the process of scale/instrument development; and strategies for data screening and dealing with nonnormally distributed data."--Larry Price, Doctoral Program in Education, Texas State University-San Marcos
Review
"For each chapter, Brown provides a comprehensive review of the topic by providing a clear commentary on the issues. He enhances this commentary with equations where necessary, illustrations, and numerical examples....The book delivers on its promise. It provides a comprehensive review of CFA techniques as a collection of essential tools that serve the contemporary researcher....The statistically sophisticated reader is provided with a current review of the appropriate use of these techniques....It could be used in an upper level graduate methodology course or by the active researcher who wishes to expand his or her repertoire of empirical techniques."--PsycCRITIQUES
Review
"This user-friendly guide to confirmatory factor analysis provides information and examples to help students and researchers through most any methodological situation. An abundance of practical advice on options for analyses, data issues, and reading and interpreting the data output make this a useful guide for almost anyone. Graduate students will find this an especially worthwhile addition to their statistical education and it would be a valuable course textbook for professors...4 stars!"--Doody's Review Service
Synopsis
With its emphasis on practical and conceptual aspects, rather than mathematics or formulas, this accessible book has established itself as the go-to resource on confirmatory factor analysis (CFA). Detailed, worked-through 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 (
www.guilford.com/brown3-materials) offers data and program syntax files for most of the research examples, as well as links to CFA-related 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.
Synopsis
Emphasizing practical and theoretical aspects of confirmatory factor analysis (CFA) rather than mathematics or formulas, Timothy A. Brown uses rich examples derived from the psychology, management, and sociology literatures to provide in-depth treatment of the concepts, procedures, pitfalls, and extensions of CFA methodology. Chock full of useful advice and tables that outline the procedures, the text shows readers how to conduct exploratory factor analysis (EFA) and understand similarities to and differences from CFA; formulate, program, and interpret CFA models using popular latent variable software packages such as LISREL, Mplus, Amos, EQS, and SAS/CALIS; and report results from a CFA study. Also covered are extensions of CFA to traditional IRT analysis, methods for determining necessary sample sizes, and new CFA modeling possibilities, including multilevel factor models and factor mixture models. Special features include a Web page offering data and program syntax files for many of the research examples so that readers can practice the procedures described in the book with real data. The Web page also includes links to additional CFA-related resources.
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 grant-supported 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.
Table of Contents
Contents
1. Introduction
Uses of Confirmatory Factor Analysis
Psychometric Evaluation of Test Instruments
Construct Validation
Method Effects
Measurement Invariance Evaluation
Why a Book on CFA?
Coverage of the Book
Other Considerations
Summary
2. The Common Factor Model and Exploratory Factor Analysis
Overview of the Common Factor Model
Procedures of EFA
Factor Extraction
Factor Selection
Factor Rotation
Factor Scores
Summary
3. Introduction to CFA
Similarities and Differences of EFA and CFA
Common Factor Model
Standardized and Unstandardized Solutions
Indicator Cross-Loadings/Model Parsimony
Unique Variances
Model Comparison
Purposes and Advantages of CFA
Parameters of a CFA Model
Fundamental Equations of a CFA Model
CFA Model Identification
Scaling the Latent Variable
Statistical Identification
Guidelines for Model Identification
Estimation of CFA Model Parameters
Illustration
Descriptive Goodness-of-Fit Indices
Absolute Fit
Parsimony Correction
Comparative Fit
Guidelines for Interpreting Goodness-of-Fit Indices
Summary
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
Model Specification
Substantive Justification
Defining the Metric of Latent Variables
Data Screening and Selection of the Fitting Function
Running the CFA Analysis
Model Evaluation
Overall Goodness of Fit
Localized Areas of Strain
Residuals
Modification Indices
Unnecessary Parameters
Interpretability, Size, and Statistical Significance of
the Parameter Estimates
Interpretation and Calculation of CFA Model Parameter
Estimates
CFA Models with Single Indicators
Reporting a CFA Study
Summary
Appendix 4.1. Model Identification Affects the
Standard Errors of the Parameter Estimates
Appendix 4.2. Goodness of Model Fit Does Not Ensure
Meaningful Parameter Estimates
Appendix 4.3. Example Report of the Two-Factor CFA
Model of Neuroticism and Extraversion
5. CFA Model Revision and Comparison
Goals of Model Respecification
Sources of Poor-Fitting CFA Solutions
Number of Factors
Indicators and Factor Loadings
Correlated Errors
Improper Solutions and Nonpositive Definite Matrices
EFA in the CFA Framework
Model Identification Revisited
Equivalent CFA Solutions
Summary
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 Uniqueness Models
Other CFA Parameterizations of MTMM Data
Consequences of Not Modeling Method Variance and
Measurement Error
Summary
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
CFA in Multiple Groups
Overview of Multiple-Groups Solutions
Multiple-Groups CFA
Selected Issues in Single- and Multiple-Groups CFA
Invariance Evaluation
MIMIC Models (CFA with Covariates)
Summary
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
Schmid-Leiman Transformation
Scale Reliability Estimation
Point Estimation of Scale Reliability
Standard Error and Interval Estimation of Scale
Reliability
Models with Formative Indicators
Summary
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 Missing Data Strategies
CFA with Non-Normal or Categorical Data
Non-Normal, Continuous Data
Categorical Data
Other Potential Remedies for Indicator Non-Normality
Summary
10. Statistical Power and Sample Size
Overview
Satorra-Saris Method
Monte Carlo Approach
Summary and Future Directions in CFA
Appendix 10.1. Monte Carlo Simulation in Greater Depth:
Data Generation