Confirmatory Factor Analysis for Applied Research

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

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