Confirmatory Factor Analysis for Applied Research

by Timothy A. Brown PsyD

Overview

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.

Product Details

ISBN-13:	9781462517817
Publisher:	Guilford Publications, Inc.
Publication date:	12/29/2014
Series:	Methodology in the Social Sciences Series
Sold by:	Barnes & Noble
Format:	eBook
Pages:	462
File size:	7 MB

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

l. IntroductionUses 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 AnalysisOverview of the Common Factor Model                                                               Procedures of EFA                                                                         Factor Extraction                                                                                             Factor Selection                                                                                             Factor Rotation                                                                                                          Factor Scores                                                                                                 Summary                                                                                                               3. Introduction to CFASimilarities 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 ModelsAn 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 ComparisonGoals 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 FrameworkExploratory SEM                               Model Identification Revisited                                                                            Equivalent CFA Solutions                                                                                    Summary                                                                                                               6. CFA of Multitrait-Multimethod MatricesCorrelated 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 StructuresOverview 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 ReliabilityEvaluation, and Formative IndicatorsHigher-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 DataCFA 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 SizeOverview                                                                                                                     Satorra-Saris Method                                                                                                Monte Carlo Approach                                                                                              Summary                                                                                                                    Appendix 10.1. Monte Carlo Simulation in Greater Depth: Data Generation          11. Recent Developments Involving CFA ModelsBayesian 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                                          ReferencesAuthor IndexSubject IndexAbout the Author

Interviews

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

Editorial Reviews

"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

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