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Confirmatory Factor Analysis for Applied Research, Second Edition,9781462515363

Confirmatory Factor Analysis for Applied Research, Second Edition

Edition: 2nd
Format: Paperback
Pub. Date: 1/8/2015
Publisher(s): The Guilford Press
Availability: This title is currently not available.


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 ( 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.

Author Biography

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. 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 CFA in Different Software Programs                                                                           
     Model Evaluation                                                                                                            
            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
         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                                                                                   
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                                                           
            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
            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                                                                                   
            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                                                                                  
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                              
10. Statistical Power and Sample Size
            Satorra–Saris Method                                                                                               
            Monte Carlo Approach                                                                                             
            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                                                                                                    
     Appendix 11.1. Numerical Example of Bayesian Probability                                         
Author Index
Subject Index
About the Author

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