Longitudinal Structural Equation Modeling

Todd D. Little

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 Readingsá

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