A Beginner's Guide to Structural Equation Modeling with LISREL, Mplus, and R

Table of Contents

Preface
Book Website
Learning SEM
Book Approach
New to the 6th Edition
Acknowledgements
About the Authors
Dedication

Chapter 1 – Introduction

What Is Structural Equation Modeling?
History of Structural Equation Modeling
Why Conduct Structural Equation Modeling?
Structural Equation Modeling Software
SEM in Statistical Packages
AMOS (SPSS)
PROC CALIS (SAS)
SEM (STATA)
SEPATH (Statistica)
SEM stand-alone Software
EQS
JMP – SAS Interface
Mplus
SEM Free Software
OpenMX – R interface
R
Latent GOLD
Software Considerations
Exercises
References

Chapter 2 - SEM Modeling Steps

SEM Modeling Steps Explained
Model Specification
Model Identification
Model Estimation
Model Testing
Table of Model Fit Indices
Parameter Statistical Significance
Model Comparison
Information Criteria for Non-nested Models
Model Modification
Modification Indices
Expected Parameter Change
MIs and EPCs in LISREL, Mplus, and R
Summary
Chapter Footnote
Exercises
References

Chapter 3 - Data Complexity

Data Access
Sample Size and Power
semPower R code to calculate sample size
Measurement Scale
Restriction of Range
Skewness
Missing Data
Outliers
Non-normality
Summary
Exercises
References
PDF Article References*

Chapter 4 - Correlation and Regression

Types of Correlation Coefficients
Factors Affecting Correlation Coefficients
Nonlinearity
Missing Data
Level of Measurement and Restriction of Range
Non-Normality
Outliers
Multiple Regression and Correlation
Bivariate, Part, and Partial Correlations
Multicollinearity and Suppressor Variables
Covariance and Correlation Matrix Conversion
Cov2Cor and Cor2Cov Functions In R
Correlation Matrix or Covariance Matrix Usage
Standardized or Unstandardized Results
Correction for Attenuation
Multiple Regression Model
Model specification
Model Identification
Model Estimation
Model Testing
Hypothesis Testing
Model Modification
Mplus Program
Multiple Regression Limitations
Model Specification
Measurement Error
Additive Equation
Chapter Footnote
Regression Model with Intercept Term
Exercises
References

Chapter 5 - Path Models

Path Model
Diagram Conventions
LISREL-SIMPLIS Achievement Path Model Program
Mplus Achievement Path Model Program
R Program for Achievement Path Model
R Achievement Path Model Program
Indirect Effects
Understanding Direct and Indirect Effects
Reproducing the Correlation Matrix
Total Effects and Correlation
Correlation Reproduction Standardized Example
Decomposition using an Unstandardized Example
Path Model Example
Model Specification
LISREL SIMPLIS Program
Mplus Program
R Program
Model Identification
Model Estimation
Model Testing
Residual Matrix Output
Testing Indirect Effects
Bootstrapping Standard Errors of Indirect Effects
R Bootstrap Example
Reporting Path Model Results
Path Model Assumptions and Limitations
Summary
Exercises
References

Chapter 6 – Measurement Models Part 1

Exploratory Factor Analysis
Sample Size
Number of Factors
Rotation Methods
Factor Scores
EFA vs PCA
LISREL-SIMPLIS EFA Example
Mplus EFA Program
EFA Program in R with the Psych Package
Pattern and Structure Matrices
Confirmatory Factor Analysis
CFA Example
Model specification
Model identification
Model Estimation
LISREL-SIMPLIS Program
Model Testing
Model Modification
Mplus Program
R Software Program
Lavaan Computer Output
CFA with Missing Continuous Data
LISREL-SIMPLIS CFA Model with Missing Data
Mplus Program-CFA Model with Missing Data
CFA with Mean Structure
LISREL-SIMPLIS Modified Program
CFA Caveats
CFA with Missing Ordinal Indicators
LISREL-SIMPLIS Program with Missing Ordinal Indicators
Mplus Program with Missing Ordinal Indicators
lavaan Program with Missing Ordinal Indicators
Model Comparisons
Summary
Exercise
References

Chapter 7 – Measurement Models Part 2

Second-Order Factor Model
Model Specification
Model Identification
Model Estimation
Model Testing
Model Modification
Model Interpretation
Bifactor Model
Model Specification
Model Identification
Model Estimation
Model Testing
Model Modification
Model Interpretation
Model Comparisons Between the Second-Order and Bifactor Models
R Program - Second-Order Factor Model
R Second-Order Factor Model Output
R Program Bifactor Model
R Bifactor Program Output
Summary
Exercise
References

Chapter 8 - Multiple Group Models

Brief Summary of Multiple Group Modeling
Multiple Group Path Analysis Model
Model Identification in Separate Groups
Model Estimation in Separate Groups
Model Testing in Separate Groups
Model Identification (Baseline multiple group model – no equality constraints)
LISREL-SIMPLIS Program
Mplus Program
R lavaan Program
Model Testing Baseline Multiple Group Model – no equality constraints
Model Identification Multiple Group Model – with equality constraints
Model Estimation Multiple Group Model – with equality constraints
LISREL-SIMPLIS Program
Mplus Program
R lavaan Program
Model Testing Multiple Group Model – with equality constraints
Model Modification
LISREL-SIMPLIS Modified Program
Mplus Modified program
R lavaan Modified Program
Model Modification – Partial Invariance Model
Multiple Group Model Interpretation
Multiple Group CFA Measurement Model
Measurement Invariance
Multiple Group CFA Example
Model Identification in Separate Groups
LISREL SIMPLIS Model Estimation in Separate Groups
Mplus Model Estimation in Separate Groups
R lavaan Model Estimation in Separate Groups
Model Testing in Separate Groups
Model Identification - Configural CFA model – no equality constraints
Model Estimation - Configural CFA model – no equality constraints
Model Testing - Configural CFA model – no equality constraints
Model Identification - Metric Multiple Group CFA Model
Model Estimation - Metric Multiple Group CFA Model
Model Testing Metric Multiple Group CFA Model
Model Modification Metric Multiple Group CFA Model
Model Identification – Scalar (strong invariance) Multiple Group CFA Model
Model Estimation - Scalar (strong invariance) Multiple Group CFA Model
Model Testing - Scalar (strong invariance) Multiple Group CFA Model
Final Model Interpretation
Structural Model Group Differences
Multiple Group Models with Ordinal Indicators
Invariance Testing Cautions
Summary
Exercise
References

Chapter 9 – Structural Equation Models Part 1

Structural Equation Models
Structural Equation Model Example
Model Specification – SEM Educational Achievement
Model Identification – SEM Educational Achievement
Model Estimation – SEM Educational Achievement
Model Testing – SEM Educational Achievement
LISREL - SIMPLIS SEM PROGRAM
Model Modification – SEM Educational Achievement
LISREL - SIMPLIS Modified Program
Mplus Modified Program
R Modified Program
Structural Equation Model with Covariate Variables (MIMIC Model)
R lavaan Program
SEM Model Interpretation
SEM Longitudinal Model – Exercise Behavior
Model Identification – SEM Longitudinal Model
Model Estimation – SEM Longitudinal Model
LISREL-SIMPLIS SEM Measurement Model
Mplus SEM Measurement Model
R lavaan SEM Measurement Model
Model Testing – SEM Measurement Model
Summary
Exercises
References

Chapter 10 – Structural Equation Models Part 2

Hypothesis Testing
Parameter Significance Test
Power and Sample Size - RMSEA
Power (RMSEA) - R code
Sample Size (RMSEA) – R code
Model Fit Chi-Square
Two-Step Versus Four-Step SEM Model Approach
Best Practices in SEM
Checklist for Structural Equation Modeling
Model Specification
Model Identification
Data Preparation
Model Estimation
Model Testing
Model Modification
Summary
Exercise
References

Chapter 11 – Reproducing SEM Article Results

First SEM Journal Article Example
First LISREL_SIMPLIS Program
First SEM Article Results
First Article Interpretation
Second SEM Journal Article Example
Second LISREL- SIMPLIS Program
Second Article Interpretation
Third SEM Journal Article Example
Third LISREL-SIMPLIS Program
Modified Second-Order Factor Model
Third Article Interpretation
Summary
Exercise
References

Chapter 12 – SEM Monte Carlo Methods

Method 1 – Generate Population Data from Random Numbers
LISREL SIMPLIS Program - Covariance Matrix
R Program Method 1
Method 2 – Generate Population Data from Covariance Matrix
Cholesky Decomposition Approach
Program 1 – Create Population Matrix
Program 2 – Generate Multivariate Normal Variables
Program 3 – Use Population Covariance Matrix in Model
Pattern Matrix Approach
R Program Method 2
Mplus Program Method 2
Method 3 - Generate Covariance Matrix from Population Model
R Program to Compute Population Covariance Matrix
R Program Method 3
Mplus Method 3
Summary
Exercise
References

Basic Matrices in SEM
Greek Symbols in SEM
Name Index
Subject Index

Biography

Randall E. Schumacker is Professor of Educational Research at the University of Alabama, USA, where he teaches courses in multiple regression, multivariate statistics, and structural equation modeling.

Tiffany A. Whittaker is Department Chair in the Department of Educational Psychology at the University of Texas at Austin, USA, where she teaches courses in structural equation modeling, statistical analysis for experimental data, and advanced statistical modeling.