This updated edition provides an essential how-to guide on the application of structural equation modeling (SEM) techniques with the AMOS software, focusing on the practical applications of both simple and advanced topics.
Written in an easy-to-understand conversational style, the book covers everything from data collection and screening to confirmatory factor analysis, structural model analysis, mediation, moderation, and more advanced topics such as mixture modeling, censored date, and non-recursive models. Through step-by-step instructions, screen shots, and suggested guidelines for reporting, Collier cuts through abstract definitional perspectives to give insight on how to actually run analysis. Unlike other SEM books, the examples used will often start in SPSS and then transition to AMOS so that the reader can have full confidence in running the analysis from beginning to end. Best practices are also included on topics like how to determine if your SEM model is formative or reflective, making it not just an explanation of SEM topics, but a guide for researchers on how to develop a strong methodology while studying their respective phenomenon of interest.
With a focus on practical applications of both basic and advanced topics, and with detailed work-through examples throughout, this book is ideal for experienced researchers and beginners across the behavioral and social sciences.
Table of Contents:
Preface
Acknowledgments
1 Introduction to Structural Equation Modeling
What Is Structural Equation Modeling? 1 Basics of SEM Input: The Covariance Matrix 2 Correlations Between Constructs
Is SEM Causal Modeling? 6
A Confirmatory Approach to SEM 7 Theory Should Lead Conceptualization 8 Assumptions of SEM 8
SEM Software 9
Understanding Diagram Symbols 9 Independent vs. Dependent Latent Variables 11 How to Measure an Unobserved Construct 11 Greek Notation and SEM 13
2 Data Screening, Assessing Reliability, Validity, and Identification 17
Data Screening 17
Screening for Impermissible Values in the Data 19 How Do I Assess If I Have Missing Data? 21 How Do I Address Missing Data? 23
Assessing Reliability 25
Identification with SEM Models 29
How Do I Calculate the Degrees of Freedom? 30 What Do I Do if My Model Is Under-Identified? 32 Sample Size: How Much Is Enough? 33 Understanding the Validity of Measures 33
3 Understanding the AMOS Program 36
Overview of the AMOS Graphics Window 36
AMOS Functions Listed as Icons in Pinned Ribbon 38
Tips to Using AMOS More Efficiently 53 Quick Reference to AMOS Functions 59
4 Measurement Model Analysis 62
Introduction to Confirmatory Factor Analysis 62 How Is a CFA Different From an EFA? 63 Interpretation of Factor Loadings 64
Setting the Metric 65
Model Fit and Fit Statistics 65 Modification Indices 68
CFA Example in AMOS 71
Addressing Missing Data in AMOS ??
Assessing Convergent and Discriminant Validity of Your Measures 83 If I Have a Weak Factor Loading, Should I Drop It? 87
How to Calculate Composite Reliability 87
How to use AI to Quickly Assess the Validity of your Data 87
What If I Have a Standardized Factor Loading Greater Than 1? 88 How Do I Report My CFA Results? 89
How to use AI to Generate CFA Tables for a Publication ??
Measurement Model Invariance Across Groups 90
Full vs. Partial Metric Invariance 98
How Do I Know Which Parameter to Free in a Partial Invariance Test? 98
Common Method Bias 102
What If My Test for Common Method Bias Is Significant? 108 What if My Common Method Bias Test Is Non-Significant? 109 What Is a Second Order Confirmatory Factor Analysis Model? 109 Reflective vs. Formative Indicators 110
Potential Identification Problems with Formative Indicators 113 Dependent Relationships with Formative Constructs 115 Higher Order Formative Construct Example 116
How Do I Present the Result of My Higher Order Formative Model? 122
Error Messages in AMOS 122
5 Path and Full Structural Models 128
Path Analysis 128
Can I Use a Correlation Matrix as My Data Input? 133 Full Structural Model Analysis 137
How Do I Report My Full Structural Model Results? 142
How to use AI to Present Structural Model Results ??
Using Specification Search to Aid in Model Trimming and Fit 143
What Are Alternative Models, and Why Should I Be Concerned With Them? 146 How Do I Add a Control Variable to My Structural Model? 147
Two Group Analysis 149
What if I Have More Than Two Groups in My Analysis? 161
Multi-level Modeling in AMOS ??When I Try to Run My Structural Analysis, I Get an Error Message About My Matrix Not Being Positive Definite 161
Can I Correlate the Error Terms of Two Unobservable Constructs in a Full Structural Model? 162
How Do I Present the Results of My Two Group Analysis? 162
How Do I Search for Multivariate Outliers? 162
How Do I Determine if My Data Is Not Normally Distributed (Non-Normal)? 165
What if I Get an Error Message in the Analysis That Says “Iteration Limit Reached”?
6 Mediation
Introduction to Mediation 170 How to Test for Mediation 172
How Do I Report the Results of My Mediation Test? 180
How to use AI to Create Mediation Tables Ready for Publication? ??
Can I Use a Correlation Matrix or Summary Data to Test Mediation in AMOS?
What if I Have Multiple Mediators in My Model? 182 How Do I Test Serial Mediation? 188
Setting the Seed in Bootstrapping
7 Moderation
Introduction to Moderation 197 Probing the Interaction 202
Testing Moderation in a Full Structural Model 207 How Do I Present My Moderation Results? 219 Mean Center vs. Z Score in Moderation Testing 221
Moderation Testing with a Categorical Moderator 223
Calculating Categorical Moderation via Pairwise Parameter Comparison 227
Moderated Mediation with a Continuous Moderator 229
How Do I Report the Results of My Moderated Mediation Test? 234
Moderated Mediation with a Categorical Moderator 234 197
8 Using Categorical Independent Variables in SEM
Binary Categorical Variables in SEM 240
Mediation with Binary Categorical Independent Variables 242 Multicategorical Independent Variables in SEM 244 Mediation with Multicategorical Independent Variables 247
Moderated Mediation with a Multicategorical Independent Variable 251
How Do I Report the Results of My Multicategorical Moderated Mediation Test?
9 Latent Growth Curve Models
Introduction to Latent Growth Curve Models ??
Including Predictors Into a Latent Growth Curve Model ??
How Do I Present My Latent Growth Curve Results? ??
Latent Growth Curves with Nonlinear Patterns ??
Latent Growth Curves Across Two Domains ??
10 Advanced Topics in SEM
Assessing Statistical Power in Structural Equation Modeling ??
How to use AI to Calculate a Global Model-fit Power Analysis ??
Determining Power via Parameter Assessments using G*Power ??
Endogeneity in SEM Models ??
Non-Recursive Models (Feedback Loops) ??
Using Weighted Scores in AMOS ??
How to Use Bootstrapping to Account for Non-Normal Data 287
Mixture Modeling 293
Analyzing Censored Data 302
Using Specification Search to Perform Exploratory Factor Analysis 317
How to Use the Program Editor to Conceptualize Your Model and Run the Analysis 338
