---

---

“Very helpful tables are used to summarize each step of a method or procedure….Chapter 3 is the heart of the textbook. It is a beautiful introduction to CFA….Summaries at the beginning and end of each chapter, an extensive number of substantive examples, figures and tables, appendices, software input and output files, as well as a sophisticated structure…make each chapter very easy to follow….Provides readers with clear recommendations and guidelines of how to deal with problems as well as a comprehensive overview of the most important aspects of CFA that an applied researcher should know. Given these outstanding qualities, I strongly believe that [this text] will continue to have a strong impact on applied researchers…and graduate students. The first edition has become a benchmark textbook in the field of introductory psychometrics, and the carefully revised second edition will widen its readership and make an impact very soon.”

—Journal of Educational and Behavioral Statistics


“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

---

Table of Contents

l. 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 CFA in Different Software Programs

Model Evaluation

Overall Goodness of Fit

Localized Areas of Strain

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. 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

Intermediate Steps for Further Developing a Measurement Model for CFA

EFA in the CFA Framework

Exploratory SEM

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

The Effects Coding Approach to Scaling Latent Variables

CFA in Multiple Groups

Overview of Multiple-Groups Solutions

Multiple-Groups CFA

Selected Issues in Single- and Multiple-Groups CFA Invariance Evaluation

MIMIC Modeling (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

Bifactor Models

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 Strategies for Missing Data

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

Appendix 10.1. Monte Carlo Simulation in Greater Depth: Data Generation

11. Recent Developments Involving CFA Models

Bayesian CFA

Bayesian Probability and Statistical Inference

Priors in CFA

Applied Example of Bayesian CFA

Bayesian CFA: Summary

Multilevel CFA

Summary

Appendix 11.1. Numerical Example of Bayesian Probability

References

Author Index

Subject Index

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 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.

---

Audience

Applied researchers in psychology, education, management/marketing, sociology, public health, and other behavioral and social sciences; graduate-level students.

---

Course Use

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.

---

Previous editions published by Guilford:

First Edition, © 2006
ISBN: 9781593852740

---

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.