Longitudinal structural equation modeling

1 Overview and Foundations of Structural Equation Modeling	p. 1
An Overview of the Conceptual Foundations of SEM	p. 2
Concepts, Constructs, and Indicators	p. 2
From Concepts to Constructs to Indicators to Good Models	p. 3
Sources of Variance in Measurement	p. 5
Classical Test Theorem	p. 6
Expanding Classical Test Theorem	p. 8
Characteristics of Indicators and Constructs	p. 9
Types of Indicators and Constructs	p. 10
Categorical versus Metrical Indicators and Constructs	p. 12
Types of Correlation Coefficients That Can Be Modeled	p. 13
A Simple Taxonomy of Indicators and Their Roles	p. 14
Reseating Variables	p. 17
Parceling	p. 20
What Changes and How?	p. 25
Some Advice for SEM Programming	p. 27
Philosophical Issues and How I Approach Research	p. 29
Summary	p. 32
Key Terms and Concepts Introduced in This Chapter	p. 33
Recommended Readings	p. 35
2 Design Issues in Longitudinal Studies	p. 37
Timing of Measurements and Conceptualizing Time	p. 37
Cross-Sectional Design	p. 39
Single-Cohort Longitudinal Design	p. 40
Cross-Sequential Design	p. 41
Cohort-Sequential Design	p. 42
Time-Sequential Design	p. 42
Other Validity Concerns	p. 43
Temporal Design	p. 47
Lags within the Internal of Measurement	p. 49
Episodic and Experiential Time	p. 49
Missing Data Imputation and Planned Missing Designs	p. 52
Missing Data Mechanisms	p. 53
Recommendations and Caveats	p. 57
Planned Missing Data Designs in Longitudinal Research	p. 60
Modeling Developmental Processes in Context	p. 62
Summary	p. 66
Key Terms and Concepts Introduced in This Chapter	p. 66
Recommended Readings	p. 69
3 The Measurement Model	p. 71
Drawing and Labeling Conventions	p. 71
Defining the Parameters of a Construct	p. 75
Scale Setting	p. 79
Identification	p. 85
Adding Means to the Model: Scale Setting and Identification with Means	p. 90
Adding a Longitudinal Component to the CFA Model	p. 94
Adding Phantom Constructs to the CFA Model	p. 96
Summary	p. 102
Key Terms and Concepts Introduced in This Chapter	p. 102
Recommended Readings	p. 104
4 Model Fit, Sample Size, and Power	p. 106
Model Fit and Types of Fit Indices	p. 106
Statistical Rationale	p. 107
Modeling Rationale	p. 108
The Longitudinal Null Model	p. 112
Summary and Cautions	p. 118
Sample Size	p. 119
Power	p. 127
Summary	p. 134
Key Terms and Concepts Introduced in This Chapter	p. 134
Recommended Readings	p. 136
5 The Longitudinal CFA Model	p. 137
Factorial Invariance	p. 137
A Small (Nearly Perfect) Data Example	p. 143
Configural Factorial Invariance	p. 143
Weak Factorial Invariance	p. 145
Strong Factorial Invariance	p. 148
Evaluating Invariance Constraints	p. 154
Model Modification	p. 156
Partial Invariance	p. 158
A Larger Example Followed by Tests of the Latent Construct Relations	p. 160
Testing the Latent Construct Parameters	p. 167
An Application of a Longitudinal SEM to a Repeated-Measures Experiment	p. 170
Summary	p. 176
Key Terms and Concepts Introduced in This Chapter	p. 177
Recommended Readings	p. 179
6 Specifying and Interpreting a Longitudinal Panel Model	p. 180
Basics of a Panel Model	p. 181
The Basic Simplex Change Process	p. 184
Building a Panel Model	p. 189
Covariate/Control Variables	p. 190
Building the Panel Model of Positive and Negative Affect	p. 191
Illustrative Examples of Panel Models	p. 198
A Simplex Model of Cognitive Development	p. 198
Two Simplex Models of Nonlongitudinal Data	p. 201
A Panel Model of Bullying and Homophobic Teasing	p. 203
Summary	p. 205
Key Terms and Concepts Introduced in This Chapter	p. 205
Recommended Readings	p. 207
7 Multiple-Group Models	p. 209
Multiple-Group Longitudinal SEM	p. 210
Step 1 Estimate Missing Data and Evaluate the Descriptive Statistics	p. 211
Step 2 Perform Any Supplemental Analysis to Rule Out Potential Confounds	p. 212
Step 3 Fit an Appropriate Multiple-Croup Longitudinal Null Model	p. 215
Step 4 Fit the Configural Invariant Model across Time and Groups	p. 216
Step 5 Test for Weak Factorial (Loadings) Invariance	p. 217
Step 6 Test for Strong Factorial (Intercepts) Invariance	p. 218
Step 7 Test for Mean-Level Differences in the Latent Constructs	p. 220
Step 8 Test for the Homogeneity of the Variance-Covariance Matrix among the Latent Constructs	p. 221
Step 9 Test the Longitudinal SEM Model in Each Group	p. 222
A Dynamic P-Technique Multiple-Group Longitudinal Model	p. 227
Summary	p. 243
Key Terms and Concepts Introduced in This Chapter	p. 244
Recommended Readings	p. 245
8 Multilevel Growth Curves and Multilevel SEM	p. 246
Longitudinal Growth Curve Model	p. 247
Multivariate Growth Curve Models	p. 261
Multilevel Longitudinal Model	p. 273
Summary	p. 282
Key Terms and Concepts Introduced in This Chapter	p. 282
Recommended Readings	p. 283
9 Mediation and Moderation	p. 286
Making the Distinction between Mediators and Moderators	p. 287
Cross-Sectional Mediation	p. 290
Half-Longitudinal Mediation	p. 293
Full Longitudinal Mediation	p. 298
Moderation	p. 307
Summary	p. 321
Key Terms and Concepts Introduced in This Chapter	p. 322
Recommended Readings	p. 322
10 Jambalaya: Complex Construct Representations and Decompositions	p. 325
Multitrait-Multimethod Models	p. 325
Pseudo-MTMM Models	p. 332
Bifactor and Higher Order Factor Models	p. 339
Contrasting Different Variance Decompositions	p. 341
Digestif	p. 350
Key Terms and Concepts Introduced in This Chapter	p. 352
Recommended Readings	p. 353
References	p. 355
Author Index	p. 367
Subject Index	p. 371
About the Author	p. 386

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