Confirmatory Factor Analysis for Applied Research/ Timothy A. Brown

1 • Introduction
Uses of Confirmatory Factor Analysis
Psychometric Evaluation of Test Instruments
Construct Valiclation
Method Effects
Measurement Invariance Evaluation
Why a Book on CPA?
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
Eactor Extraction
Factor Selection
Factor Rotation
Eactor Scores
Summary
3 • Introduction to CFA
Similarities and Differences of EFA and CFA
Common Eactor Model
Standardized and Unstandardized Solutions
Indicator Cross-Loadings/Model Parsimony
Unique Variances
Model Comparison
Purposes and /Vdvantages of CPA
Parameters of a CPA Model
Pundamental Equations of a CPA Model
CPA Model Identification
Scaling the Latent Variable
Statistical Identification
Gtiidelines for Model Identification
Estimation of CPA Model Parameters
Illustration
Descriptive Goodness-of-Pit Indices
Absolute Fit
Parsimony Correction
Comparative Fit
Cuidelines for Interpreting Coodness-of-Fit Indices
Summary
Appendix 3.1. Communalilics, Model-Implied Correlalion.s, and Factor
Correlations in EPA and CPA
Appendix 3.2. Obtainitig a Solution for a Just-Identified Factor Model
Appendix 3.3. Hand Calculation of for the Figure 3.8 Path Model
4 • Specification and Interpretation of CPA Models
An Applied Example of a CPA Measurement Model
Model Specification
Sidistantive Justification
Defining the Metric of Latent Variables
Data Screening and Selection of the Pitting Punction
Running the CPA Analysis
Model Evaluation
Overall Coodness of Fit
Localized Areas of Strain
Residuals
Modification Indices
Unnecessary Parametei s
Intelprctability. Size, and Statistical Significance of the Parameter
Estimates
Interpretation and Calculation of CPA Model Parameter
Estimates
CPA Models with Single Indicators
Reporting a Cf*A Study
Sutnmary
Appendix 4.1 . Model Identification Affects the Standard Errors of the
Paratncter Pstitrtaics
Appendix 4.2. Cioodncss of Model Fit Docs Not Pnsutc Meaningful Paratncter
Estimates
Appendix 4.3. Example Report of the fwo-Factor CPA Model of Ncuroticism
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 CEA Solutions
Summary
6 • CFA of Muititraif^Multimethod Matrices
Correlated versus Random Measurement Error Revisited
The Multitrait-Multimethod Matrix
CEA Approaches to Analyzing the MTMM Matrix
Correlated Methods Models
Correlated Unicjuencss 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 Croup
Congeneric, Tau-Eqiiivalcnt, and Parallel Indicators
Longitudinal Measurement Invariance
CFA in Multiple Croups
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 CPA Models:
Higher-Order Factor Analysis, Scale Reliability
Evaluation, and Formative Indicators
Higher-Order Factor Analysis
Sccond-Ordcr Factor Analysis
Schmid-Lciman Transformation
Scale Reliability Estimation
Point Estimation oj Scale Reliability
Standard Error and Intenal Estimation of Scale Reliahilitv
Models with Formative Indicators
Summar\'
• Data issues in CPA:
Missing, Non-Normal, and Categorical Data
CPA with Missing Data
Mechanisms of Missing Data
Conventional Approaches to Missing Data
Recommended Missing Data Strategies
CPA with Non-Normal or Categorical Data
Non-Normal, Continuous Data
Categorical Data
Othet 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 CPA
Appendix 10.1. Monte Carlo Simulation in Greater Depth:
Data Generation