Confirmatory Factor Analysis for Applied Research

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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.
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Editorial Reviews

From the Publisher

"I found the author’s 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 I’ve 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


"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
Doody's Review Service
Reviewer: Christopher J Graver, PhD, ABPP-CN(Madigan Healthcare System)
Description: Confirmatory factor analysis is a commonly used statistical technique, but it is often forgotten in the literature. This book provides a comprehensive resource on the use of this technique from methodological approaches to statistical considerations.
Purpose: As part of the Methodology in the Social Sciences series, this book fills a significant gap in the current literature for a text on confirmatory factor analysis. It is intended to do this in a user-friendly way and spares the reader many of the behind-the-scenes complexities that are not critical to know on a day-to-day basis.
Audience: The author intends this book for graduate students and researchers in the social and behavioral sciences (e.g., psychology, sociology, education, political science, etc.). The author has a respectable scholarly record and serves as a statistical consultant on federally funded research projects.
Features: The book begins with an introduction to confirmatory factor analysis for those new to this technique. It then helps readers to run, view, and interpret the data from this technique. Later chapters begin to explore specialized uses of the confirmatory factor analysis. The book ends with chapters addressing data issues (e.g., missing data, non-normality, data parsing) and statistical power and sample size considerations. Each chapter begins with an abstract and ends with a summary, both of which are helpful at a glance. Numerous figures and tables summarize the information and provide example statistical outputs to assist readers. The practical examples aid in comprehending this material from a hands-on point of view.
Assessment: 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.
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Product Details

Meet the Author

Timothy A. Brown is a professor in the Department of Psychology at Boston University (BU), and Director of Research at BU's Center for Anxiety and Related Disorders. He has published extensively in the areas of the classification of anxiety and mood disorders, psychometrics, and methodological advances in social sciences research.
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Table of 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
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
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
Descriptive Goodness-of-Fit Indices
Absolute Fit
Parsimony Correction
Comparative Fit
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
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
Modification Indices
Unnecessary Parameters
Interpretability, Size, and Statistical Significance of the Parameter Estimates
Interpretation and Calculation of CFA Model Parameter
CFA Models with Single Indicators
Reporting a CFA Study
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
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
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)
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
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 Missing Data Strategies
CFA with Non-Normal or Categorical Data
Non-Normal, Continuous Data
Categorical Data
Other Potential Remedies for Indicator Non-Normality
10. Statistical Power and Sample Size
Satorra-Saris Method
Monte Carlo Approach
Summary and Future Directions in CFA
Appendix 10.1. Monte Carlo Simulation in Greater Depth:
Data Generation
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