There has been considerable attention to making the methodologies of structural equation modeling available to researchers, practitioners, and students along with commonly used software. Structural Equation Modelling Using R/SAS aims to bring it all together to provide a concise point-of-reference for the most commonly used structural equation modeling from the fundamental level to the advanced level. This book is intended to contribute to the rapid development in structural equation modeling and its applications to real-world data. Straightforward explanations of the statistical theory and models related to structural equation models are provided, using a compilation of a variety of publicly available data, to provide an illustration of data analytics in a step-by-step fashion using commonly used statistical software of R and SAS. This book is appropriate for anyone who is interested in learning and practicing structural equation modeling, especially in using R and SAS. It is useful for applied statisticians, data scientists and practitioners, applied statistical analysts and scientists in public health, and academic researchers and graduate students in statistics, whilst also being of use to R&D professionals/practitioners in industry and governmental agencies.
Key Features:
- Extensive compilation of commonly used structural equation models and methods from fundamental to advanced levels
- Straightforward explanations of the theory related to the structural equation models
- Compilation of a variety of publicly available data
- Step-by-step illustrations of data analysis using commonly used statistical software R and SAS
- Data and computer programs are available for readers to replicate and implement the new methods to better understand the book contents and for future applications
- Handbook for applied statisticians and practitioners
Author(s): Ding-Geng Chen, Yiu-Fai Yung
Publisher: CRC Press/Chapman & Hall
Year: 2023
Language: English
Pages: 428
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Table of Contents
List of Figures
Preface
Authors
1 Linear Regression to Path Analysis
1.1 Descriptive Data Analysis
1.1.1 Data and Summary Statistics
1.1.2 Preliminary Graphical Analysis
1.2 Review of Multiple Linear Regression Model
1.2.1 Multiple Linear Regression Model
1.2.2 The Method of Least Squares Estimation (LSE)
1.2.3 The Properties of LSE
1.2.3.1 Unbiasedness
1.2.3.2 The Predicted Values
1.2.3.3 The Residuals for Diagnostics
1.2.3.4 Residual Sum of Squares (RSS)
1.2.3.5 Variance Estimate
1.2.3.6 R[sup(2)]
1.2.4 Assumptions in Regression Models
1.3 Path Analysis Model
1.3.1 Implied Covariance Structures of a Simple Path Model
1.3.2 What Does It Mean by Modeling a Covariance Structure?
1.3.3 Discrepancy Functions for Parameter Estimation and Model Fitting
1.3.4 Evaluation of the Structural Model and the Goodnessof-Fit Statistics
1.3.4.1 χ[sup(2)] Test of Model Fit
1.3.4.2 Loglikelihood
1.3.4.3 Root Mean Square Error of Approximation (RMSEA) (Steiger and Lind, 1980) and the Standardized Root Mean Square Residual (SRMR)
1.3.4.4 Comparative Fit Index (CFI) (Bentler, 1995)
1.3.4.5 Tucker-Lewis Fit Index (TLI) (Tucker and Lewis, 1973)
1.3.4.6 The Akaike's Information Criterion (AIC) (Akaike, 1987) and the Bayesian Information Criterion (BIC) (Raftery, 1993; Schwarz, 1978)
1.3.4.7 Which Goodness-of-Fit Indices to Use?
1.4 Data Analysis Using R
1.4.1 Multiple Linear Regression
1.4.2 Path Analysis
1.5 Data Analysis Using SAS
1.6 Discussions and Further Readings
1.7 Exercises
2 Latent Variables—Confirmatory Factor Analysis
2.1 Data Descriptions
2.1.1 Maslach Burnout Inventory
2.1.2 HolzingerSwineford1939
2.2 CFA Model and Estimation
2.2.1 The CFA Model
2.2.2 Covariance Structure Parameters of the CFA Model
2.2.3 Covariance Structure Parameters and Model Matrices
2.2.4 Covariance Structures of the CFA Model and its Estimation
2.2.5 Estimation of Mean and Covariance Structure Parameters
2.2.6 CFA Model for MBI Data
2.2.6.1 Measurement Model for Latent Variable EE
2.2.6.2 Measurement Model for Latent Variable DP
2.2.6.3 Measurement Model for Latent Variable PA
2.2.6.4 Covariance Among the Latent Variables
2.2.6.5 Means and Variances for the Latent Variables
2.3 CFA with R Lavaan
2.3.1 Data Analysis for MBI
2.3.1.1 Fitting the Original Model
2.3.1.2 Modification Indices and Model Refitting
2.3.1.3 Final CFA Model
2.3.2 Data Analysis for HolzingerSwineford1939
2.3.2.1 Fitting the Original Three-Factor CFA Model
2.3.2.2 Modification Indices and Model Re-Fitting
2.4 CFA with SAS
2.5 Conclusions and Discussion
2.6 Exercises
3 Mediation Analysis
3.1 Industrialization and Political Democracy Data Set
3.2 Mediation Model and Statistical Inference
3.2.1 Basic Mediation Model
3.2.2 Direct, Indirect, and Total Effects: Statistical Model and Definitions
3.2.3 Estimation of Direct, Indirect and Total Effects
3.2.4 General Structural Equation Model and its Implied Structured Covariance Matrix
3.2.4.1 LISREL-Type Model
3.2.4.2 RAM-Type Model
3.2.5 Statistical Inference on Mediation Effect
3.2.5.1 Sobel Test
3.2.5.2 Bootstrap Resampling Approach
3.2.5.3 Full Mediation Versus Partial Mediation
3.3 Data Analysis Using R
3.3.1 General Structural Equation Modeling
3.3.2 Mediation Analysis
3.4 Data Analysis Using SAS
3.5 Discussions
3.6 Exercises
4 Structural Equation Modeling with Non-Normal Data
4.1 Industrialization and Political Democracy Data
4.2 Methods for Non-Normal Data
4.2.1 Parameter Estimations
4.2.2 Statistical Inferences and Testing by ML Estimation with Adjustments
4.3 Data Analysis Using R
4.4 Data Analysis Using SAS
4.5 Discussions
4.6 Exercises
5 Structural Equation Modeling with Categorical Data
5.1 Exploratory Data Analysis
5.2 Model and Estimation
5.2.1 The Threshold Model for Ordered Categorical Responses
5.2.2 Modeling Endogenous and Exogenous Categorical Variables in SEM
5.2.3 The Covariance Structures
5.2.4 The Fitting of Covariance Structures in Samples
5.2.5 The Diagonally Weighted Least Squares (DWLS) Discrepancy Function for Parameter Estimation
5.2.6 A Note About the Parameterization Related to the Latent Propensity Responses
5.2.7 Some Practical Assumptions
5.3 Data Analysis Using R
5.3.1 The CFA Model
5.3.2 Model Fitting with MLE Assuming Normal Distribution - MLE Estimation
5.3.3 Model Fitting with Robust MLE
5.3.4 Model Fitting Accounting for Categorization - WLSMV Estimator
5.3.5 Comparison Among MLE, MLR and WLSMV
5.4 Data Analysis Using SAS
5.5 Discussions
5.6 Exercises
6 Multi-Group Data Analysis: Continuous Data
6.1 Data Descriptions
6.2 Model and Estimation
6.2.1 Unconstrained θ[sub(g)]'s Across Groups: Configural Invariance Model
6.2.2 Completely Constrained θ[sub(g)]'s Across Groups: Ideal Model
6.2.3 Partial Invariance Models
6.2.4 Strategy of Multi-group Analysis
6.3 Data Analysis Using R
6.3.1 Establish Group-Specific Baseline Models
6.3.2 Establish the Configural Invariance Model
6.3.3 Fit the Ideal Model
6.3.4 Partial Invariance
6.4 Data Analysis Using SAS
6.5 Discussions
6.6 Exercises
7 Multi-Group Data Analysis: Categorical Data
7.1 Data and Preliminary Analysis
7.2 CFA Models
7.2.1 Step One: The Group-Specific Model
7.2.2 Step Two: The Configural Model
7.2.3 Step Three: The Ideal Invariance
7.2.4 Testing Latent Mean Difference Between Sex
7.3 Data Analysis Using SAS
7.4 Discussions
8 Pain-Related Disability for People with Temporomandibular Disorder: Full Structural Equation Modeling
8.1 Data Description
8.2 Theoretical Model and Estimation
8.2.1 The Hypothesized Model for Pain-Related Disability
8.2.2 The Mathematical Model for Pain-Related Disability
8.2.3 Measurement and Structural Models
8.3 Data Analysis Using R
8.3.1 Validation of Measurement Models
8.3.2 Fit the Full Structural Equation Model for Pain-Related Disability
8.3.3 Plotting of the Fitted Model
8.4 Data Analysis Using SAS
8.5 Discussions
8.6 Exercises
9 Breast-Cancer Post-Surgery Assessment—Latent Growth-Curve Modeling
9.1 Data and Preliminary Analysis
9.1.1 Data Description
9.1.2 Exploratory Data Analysis
9.1.2.1 Changes in Means and Variances
9.1.3 Changes in Longitudinal Trajectories
9.2 Latent Growth-Curve Modeling
9.2.1 Latent Growth-Curve Model with a Single Outcome
9.2.2 Latent Growth-Curve Model with Multiple Outcomes
9.2.3 Latent Growth-Curve Model with Covariates
9.2.4 Modeling of Latent Growth Curves by Structural Equation Modeling
9.2.4.1 Modeling of Multiple Outcomes
9.2.4.2 Modeling with Covariates
9.3 Data Analysis Using R
9.3.1 Latent Growth-Curve Modeling for MOOD
9.3.1.1 The Basic Model for the Trajectory of Mood
9.3.1.2 Final Model for the Trajectory of Mood
9.3.2 Latent Growth-Curve Modeling for SOCADJ
9.3.2.1 The Basic Model for the Trajectory of Social Adjustment
9.3.2.2 The Final Model for the Trajectory of Social Adjustment
9.3.3 Multiple-Outcome Latent Growth-Curve Modeling
9.3.3.1 Joint LGC Models for MOOD and SOCADJ
9.3.3.2 Initial Model Fitting of the Joint Model for MOOD and SOCADJ
9.3.3.3 Model Fitting with Modification Indices
9.3.3.4 Final Model Based on Model Parsimony
9.3.4 Joint LGC Model with Covariates
9.4 Data Analysis Using SAS
9.4.1 Latent Growth Curve for the Trajectory of Mood
9.4.2 Multiple-Outcome Latent Growth- Curve Modeling
9.4.3 Joint LGC Model with Covariates
9.5 Discussions
9.6 Exercises
10 Full Longitudinal Mediation Modeling
10.1 Data Descriptions
10.2 The Full Longitudinal Mediation Model (FLMM) and the Decomposition of Total Effect
10.2.1 A Single Mediator in a Single Pathway
10.2.2 Multiple Mediators in a Single Mediation Pathway
10.2.3 Multiple Mediators in Multiple Mediation Pathways
10.2.4 Computing Specific Indirect Effects in Applications
10.2.5 Limitations
10.3 Data Analysis Using R
10.3.1 Fit the FLMM
10.3.1.1 R/Lavaan Implementation
10.3.1.2 Model Fitting Measures
10.3.1.3 Self-Enhancement Process Over Time with Auto-Regressive Effects
10.3.1.4 Cross-Lag Effects
10.3.1.5 Feedback Effects
10.3.2 Mediation Analysis
10.4 Data Analysis Using SAS
10.5 Discussions
10.6 Exercises
11 Multi-Level Structural Equation Modeling
11.1 Data Descriptions
11.2 General Concept for Multi-Level Structural Equation Modeling
11.3 Data Analysis Using R
11.4 Discussions
11.5 Exercises
12 Sample Size Determination and Power Analysis
12.1 Design Studies with Two-Treatment Comparison
12.1.1 A Brief Theory
12.1.2 R Implementation
12.1.3 Linkage to Structural Equation Modeling
12.2 Design Studies with Structure Equation Models
12.2.1 Fit the LGC Model for MOOD
12.2.2 Monte-Carlo Simulation-Based Power Calculation
12.3 Discussions
Bibliography
Index
