Longitudinal Structural Equation Modeling

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 five-day class in Structural Equation Modeling the week prior to 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.

In an effort to continually improve our instruction we obtain student evaluations with each course offering. Here is a sample of reviews from our 2016 LSEM workshop:

One of the best statistical workshops I’ve ever taken, the first where I would go home and work for additional hours analyzing data or reading the notes for greater understanding of the material.

This workshop provides clear, understandable, and engaging teaching with wonderful resources for the future. Dan and Patrick are fantastic instructors, and they provide a very comfortable, enjoyable atmosphere for a week-long stats workshop.

This is the best option for training that will effectively prepare you to foray into the method. It greatly expanded my perspective on longitudinal analysis.

Excellent instructors, a great opportunity to clarify issues that I was always unsure about, helpful and comprehensive materials that are priceless!

The instruction was first-rate. It’s no surprise Curran & Bauer are award-winning instructors.

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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...

Participants can ask text-based questions using a Zoom function that will be monitored by CBA staff and conveyed to the instructor. If a question cannot be answered during lecture, a text response will be provided at a later time.

Because participants are receiving the stream from Zoom and not broadcasting video images back, the connectivity requirements are minimal. A minimum of 150kbps (kilobytes per second) is required to participate in a video webinar, and this can be wired or wireless. Given typical home internet connections or personal WiFi access, these requirements are quite low. For example, it is recommended that a 3000kbps (or 3mbps, megabytes per second) connection be used to stream a movie on Netflix. A typical WiFi hotspot on a typical cell phone is 20-30mbps, thus any standard internet connection should allow for uninterrupted participation in the webinar. See https://www.speedtest.net/ to evaluate your own connection speed. Note that a typical source of connectivity problems in the home is linking the device to the WiFi broadcast unit, so be certain your device is has uninterrupted lines of site to the wireless modem; see, e.g., https://www.familyhandyman.com/smart-homeowner/9-simple-tips-for-faster-wi-fi/

Live-stream lectures will begin at 9:00 a.m. EST and finish at 4:00 p.m. EST each day. On Monday through Thursday, computer demonstrations will be provided from 4:00 p.m. EST to 5:00 p.m. EST, with separate breakout meetings for Mplus, R, and Stata.

There will be 15 minute morning and afternoon breaks and a one hour lunch break, the exact times of which are determined during lecture. Local time zones within which the participant is connected must be adjusted to correspond to Eastern Standard Time.

The live-stream does not have DVR-like controls and thus cannot be paused or rewound during the session itself. However, full recordings of the live-stream will be available to all participants for seven days following the completion of the workshop. The recordings cannot be saved by the participant and will not be available after the seven day period.

CBA is not able to provide technical support for end-user issues. As such, participants are fully responsible for connectivity that supports the live-stream of audio and video. Information will be provided about the minimum required bandwidth and methods for testing connectivity. However, in the low probability that a participant is not able to connect, there will be access to the recorded sessions for seven days following the completion of the workshop.

We offer reduced-price registrations for graduate students who are actively enrolled in a recognized masters or doctoral training program. No application is necessary to qualify for the student tuition rates; simply choose the student rate when beginning the registration process at the top of the page. Confirmation of student status may be requested at a later time.

We are fortunate to have the opportunity to work in collaboration with the Society of Multivariate Experimental Psychology (SMEP) to provide a limited number of financial awards to students from under-represented groups to attend methodological workshops. These awards are made to qualifying students and post doctoral fellows with available funds of up to $1000 per student. Please see Support for Students from Underrepresented Groups to Attend Methodological Workshops for full details on both of these sources of support.

Curran-Bauer Analytics will fully refund registration fees, minus transaction fees, for cancellations made with one week or more notice prior to the event. Registration fees are non-refundable if a cancellation is made less than one week before the event.

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