Longitudinal Structural Equation Modeling

Abstract

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. Part I: 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. Part II: 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. Part III: 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. Part IV: 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. Part V: 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. Part VI: 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 Manel 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. Part VII: 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. Part VIII: 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. Part IX: 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. Part X: 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.