Longitudinal Structural Equation Modeling

Chapter 1. Introduction, Summary of Traditional Models of Change, and Review of SEM
1.1 Introduction and Organization of the Workshop
1.2 Why Longitudinal Data are Needed
1.3 Raw Score Change versus Residualized Change
1.4 Traditional Methods as a Foundation for Autoregressive, Latent Change Score, & Latent Curve Models
1.5 Review of Structural Equation Models (SEMs)

Chapter 2. Longitudinal Measurement Models and Factorial Invariance
2.1 Assumptions Invoked when Modeling Manifest Variables Over Time
2.2 Measurement Invariance across Group
2.3 Measurement Invariance Over Time
2.4 The Longitudinal Confirmatory Factor Analysis Model
2.5 Defining and Testing Alternative Forms of Longitudinal Factorial Invariance

Chapter 3. The Autoregressive Cross-lagged (ARCL) Panel Model
3.1 Residualized Change as a Two Time-point Autoregressive Panel Model
3.2 Bivariate Autoregressive Cross-Lagged Models
3.3 Strengths and Limitations of the ARCL

Chapter 4. The Unconditional Linear Latent Curve Model (LCM)
4.1 Defining a Latent Growth Curve
4.2 Latent Growth Curves as a Confirmatory Factor Model
4.3 Intercept-only vs. Intercept and Linear Slope LCMs
4.4 Alternative Metrics of Time

Chapter 5. Nonlinear and Conditional Latent Curve Models
5.1 Modeling Nonlinear Trajectories: Quadratic, Piecewise, and Freed-Loading Models
5.2 Time-Invariant Covariates (TICs): Defining Main Effects and Interactions
5.3 Probing and Graphing Effects Between TICs and Growth Factors

Chapter 6. Multivariate Latent Curve Models
6.1 Time-Varying Covariates: Defining Contemporaneous and Lagged Effects
6.2 The Fully Multivariate Latent Curve Model
6.3 The Autoregressive Latent Trajectory Model (ALT)
6.4 The LCM with Structured Residuals (LCM-SR) Model

Chapter 7. Longitudinal SEMs with Non-normal and Discrete Outcomes
7.1 Outcomes that are Continuous but Non-Normal
7.2 Longitudinal SEMs with Binary and Ordinal Outcomes: Concepts
7.3 Longitudinal SEMs with Binary and Ordinal Outcomes: Estimation and Interpretation

Chapter 8. Modeling Population Heterogeneity: Part 1
8.1 Population Heterogeneity in the Conventional LCM
8.2 The Multiple Groups Growth Model
8.3 Extensions of Multiple Groups LCM

Chapter 9. Modeling Population Heterogeneity: Part 2
9.1 Growth Mixture Models: Theory
9.2 Growth Mixture Models: Specification
9.3 Class Enumeration
9.4 Model Sensitivity

Appendix. The Latent Change Score (LCS) Model
A.1 Observed Change Scores vs. Latent Change Scores
A.2 Univariate LCS Model
A.3 Bivariate LCS Model
A.4 Extensions of the LCS Model

Our workshop is designed for graduate students, post-doctoral fellows, faculty, and research scientists from the behavioral, social, and health sciences. Prior exposure to structural equation modeling is helpful, but we will also review core aspects of SEM at the start of the workshop. To have a stronger foundation in SEM, participants may wish to consider also attending our free three-day asynchronous Introduction to Structural Equation Modeling workshop prior to taking Longitudinal Structural Equation Modeling.

Software demonstrations will be provided in Mplus, R, and Stata. Note that R can be downloaded for free. While it is helpful to have some familiarity with Mplus, R, or Stata, this is not necessary. The lectures which constitute the majority of the workshop are software-independent.

Our motivating goal is to provide an intense yet enjoyable instructional experience that focuses on a large number of both introductory and advanced topics in longitudinal structural equation modeling. We strive to strike an equal balance between core concepts of the underlying statistical models along with the practical application and interpretation of longitudinal SEMs fitted to real empirical data. Our workshop is designed to provide participants with the materials and instruction needed to both develop a real understanding of the longitudinal SEM and to be able to thoughtfully apply a variety of basic and advanced models to their own data.

Dan Bauer and Patrick Curran co-teach the workshop and alternate lecturing throughout the day. Participants will receive approximately 35 hours of total lecture time as well as PDF copies of the course notes and the computer demonstrations as well as data and code for all examples. The PDFs are not time-limited and may be retained indefinitely but should not be distributed to others without obtaining prior permission.

Please see sample copies of the lecture notes (one chapter) and R demonstration notes (full copy) from our 5-day SEM class. Mplus and Stata versions parallel the R demonstration notes.

Learn more about what makes our training unique...