Longitudinal Structural Equation Modeling

Todd D. Little, PhD, is Professor of Educational Psychology and Leadership at Texas Tech University and founding Director of the Texas Tech University Institute for Measurement, Methodology, Analysis, and Policy. Dr. Little is a Fellow of the American Association for the Advancement of Science; the American Psychological Association (APA) Divisions 5, 7, and 15; and the Association for Psychological Science. He is past president of APA Division 5 (Evaluation, Measurement, and Statistics). Dr. Little organizes and teaches in his renowned Stats Camp each June. Partly because of the impact and importance of Stats Camp, Dr. Little was awarded the Cohen Award from APA Division 5 for Distinguished Contributions to Teaching and Mentoring.

PROLOGUE
* A personal introduction and what to expect
How statistics came into my life
My approach to the book
Key features of the book
Overview of the book
* Datasets and measures used
My dataset with the Inventory Felt Energy and Emotion in Life (I FEEL) measure
The I FEEL
Gallagher and Johnson's MIDUS example
Neuroticism
Negative affect
Dorothy Espelage's bullying and victimization examples
Peer victimization
Substance use
Family conflict
Family closeness
Bullying
Homophobic teasing
* Overdue gratitude
* Prophylactic apologies
1. OVERVIEW AND SEM FOUNDATIONS
* An overview of the conceptual foundations of SEM
Concepts, constructs, and indicators
From concepts to constructs to indicators to good models
* Sources of variance in measurement
Classical test theorem
Expanding classical test theorem
* Characteristics of indicators and constructs
Types of indicators and constructs
Categorical versus metrical indicators and constructs
Types of correlation coefficients that can be modeled
* A simple taxonomy of indicators and their roles
* Rescaling variables
* Parceling
* What changes and how?
* Some advice for SEM programming
* Philosophical issues and how I approach research
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
2. DESIGN ISSUES IN LONGITUDINAL STUDIES
* Timing of measurements and conceptualizing time
Cross-sectional design
Single-cohort longitudinal design
Cross-sequential design
Cohort-sequential design
Time-sequential design
Other validity concerns
Temporal design
Lags within the interval of measurement
Episodic and Experiential Time
* Missing data imputation and planned missing designs
Missing data mechanisms
Recommendations and caveats
Planned missing data designs in longitudinal research
* Modeling developmental processes in context
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
3. THE MEASUREMENT MODEL
* Drawing and labeling conventions
* Defining the parameters of a construct
* Scale setting
* Identification
* Adding means to the model: Scale setting and identification with means
* Adding a longitudinal component to the CFA model
* Adding phantom constructs to the CFA model
* Summary
* Key terms and concepts introduced in this chapter
* Recommended Readings
4. MODEL FIT, SAMPLE SIZE, AND POWER
* Model fit and types of fit indices
Statistical rationale
Modeling rationale
The longitudinal null model
Summary and cautions
* Sample Size
* Power
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
5. THE LONGITUDINAL CFA MODEL
* Factorial invariance
* A small (nearly perfect) data example
Configural factorial invariance
Weak factorial invariance
Strong factorial invariance
Evaluating invariance constraints
Model modification
Partial invariance
* A larger example followed by tests of the latent construct relations
Testing the latent construct parameters
* An application of a longitudinal SEM to a repeated-measures experiment
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
6. SPECIFYING AND INTERPRETING A LONGITUDINAL PANEL MODEL
* Basics of a panel model
* The basic simplex change process
* Building a panel model
Covariate/control variables
Building the panel model of positive and negative affect
* Illustrative examples of panel models
A simplex model of cognitive development
Two simplex models of non-longitudinal data
A panel model of bullying and homophobic teasing
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
7. MULTIPLE-GROUP MODELS
* Multiple-group longitudinal SEM
Step 1: Estimate missing data and evaluate the descriptive statistics
Step 2: Perform any supplemental analysis to rule out potential confounds
Step 3: Fit an appropriate multiple-group longitudinal null model
Step 4: Fit the configurally invariant model across time and groups
Step 5: Test for weak factorial (loadings) invariance
Step 6: Test for strong factorial invariance
Step 7: Test for mean-level differences in the latent constructs
Step 8: Test for the homogeneity of the variance–covariance matrix among the latent constructs
Step 9: Test the longitudinal SEM model in each group
* A dynamic p-technique multiple-group longitudinal model
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
8. MULTILEVEL GROWTH CURVES AND SEM
* Longitudinal growth curve model
* Multivariate growth curve models
* Multilevel longitudinal model
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
9. MEDIATION AND MODERATION
* Making the distinction between mediators and moderators
Cross-sectional mediation
Half-longitudinal mediation
Full longitudinal mediation
* Moderation
* Summary
* Key terms and concepts introduced in this chapter
* Recommended readings
10. JAMBALAYA: COMPLEX CONSTRUCT REPRESENTATIONS AND DECOMPOSITIONS
* Multitrait-multimethod models
* Pseudo-MTMM models
* Bifactor and higher order factor models
* Contrasting different variance decompositions
* Digestif
* Key terms and concepts introduced in this chapter
* Recommended readings