Longitudinal Data Analysis Using Structural Equation Modeling

A 4-Week On Demand Seminar Taught by
Paul D. Allison, Ph.D.

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To see a sample of the course slides, click here.

For the past six years, Dr. Paul Allison has been teaching his acclaimed seminar on Longitudinal Data Analysis Using Structural Equation Modeling to audiences around the world. This seminar develops a methodology that integrates two widely used approaches to the analysis of longitudinal data: cross-lagged panel analysis and fixed effects analysis. In this more comprehensive framework, you can test causal hypotheses in a way that both controls for unmeasured confounders while also allowing for reverse causation. In addition, the SEM methodology lets you relax many of the restrictive assumptions of more traditional methods. 

The course takes place in a series of four weekly installments of videos, quizzes, readings, and assignments, and requires about 6-8 hours/week. You can participate at your own convenience; there are no set times when you are required to be online. The course can be accessed with any recent web browser on almost any platform, including iPhone, iPad, and Android devices. It consists of 11 modules:

  1. Introduction
  2. Cross-Lagged Panel Models
  3. Goodness of Fit and Equality Constraints
  4. Fixed Effects with SEM
  5. Fixed Effects with Time-Invariant Predictors
  6. Combining Fixed Effects with Cross-Lagged Models
  7. One-Sided Estimation
  8. Hip Data Example
  9. Getting the Lags Right
  10. Models for Binary Outcomes
  11. Models for Count Data

The modules contain videos of the live, 2-day version of the course in its entirety. Each module is followed by a short multiple-choice quiz to test your knowledge. There are also weekly exercises that ask you to apply what you’ve learned to a real data set. 

Each week, there are two assigned articles to read. There is also an online discussion forum where you can post questions or comments about any aspect of the course. All questions will be promptly answered by Dr. Allison. 

Downloadable course materials include the following PDF files:

  • All slides displayed in the videos.
  • Exercises for each week. 
  • Readings for each week.
  • Computer code for all exercises (in SAS, Stata, Mplus and R formats).
  • A certificate of completion.


Panel data have two big attractions for making causal inferences with non-experimental data:

  • The ability to control for unobserved, time-invariant confounders.
  • The ability to determine the direction of causal relationships.

Fixed effects methods that control for unobserved confounders are now well known and widely used. Cross-lagged panel models have long been used to study the direction of causality. But trying to combine these two approaches poses serious problems.

To deal with these difficulties, econometricians have developed the Arellano-Bond methods for estimating dynamic panel data models. However, Arellano-Bond is known to be statistically inefficient and can also be severely biased in important situations.

Professor Allison and his colleagues have recently shown that dynamic panel models can easily be estimated by maximum likelihood with SEM software (ML-SEM) (Allison et al. 2017). That work demonstrates that the performance of ML-SEM is superior to the econometric methods. Plus, ML-SEM offers better capabilities for handling missing data, evaluating model fit, relaxing constraints, and allowing for non-normal data.

This seminar takes a deep dive into the ML-SEM method for estimating dynamic panel models, exploring the ins and outs of assumptions, model specification, software programming, model evaluation and interpretation of results. We’ll work through several real data sets in great detail, testing out alternative methods and working toward an optimal solution.

This is an applied course with a minimal number of formulas and a maximal number of examples. Although the methodology is cutting edge, the emphasis is on how to actually do the analysis in order accomplish your objectives. 

It’s also a hands-on course with lots of opportunities to practice the methods, including four carefully-designed exercises using real data.

Four statistical packages will be used to demonstrate the methods: Mplus, SAS, Stata, and the lavaan package for R. Wherever possible, program code for all of these packages will be included for each example. The exercises can be done with any of the four packages.

At the end of this seminar, you should be able to confidently apply the ML-SEM method for dynamic panel data to your own research projects. You will also have a thorough understanding of the rationale, assumptions, and interpretation of these methods.

CAUTION: This is not a survey course but rather an intensive study of a specific methodology—one that has enormous potential for improving causal inference from panel data. This seminar does NOT cover several popular methods that use SEM to analyze panel data, including:

  • Latent growth curve models
  • Latent trajectory models
  • Common factor models 

The methods covered in this course are NOT typically useful in analyzing data from randomized experiments. That’s because dynamic panel models are designed for situations in which the predictor variables of central interest vary over time. These methods are also not designed for prediction—rather, the goal is to maximize the ability to make valid causal inference. To use these methods, you need panel data with at least three time points, and the number of individuals should be substantially larger than the number of time points.


The methods in this course will be demonstrated with four software packages: Mplus (version 7.1 or later), Stata (version 13 or later), SAS (version 9.2 or later), and lavaan (a package for R). Whenever possible, program code for all four packages is included in the slide deck. To do the hands-on exercises, you will need access to a computer with one of these packages installed. 


This seminar is designed for those who want to analyze longitudinal data with three or more time points, and whose primary interest is in the effect of predictors that vary over time. You should have a solid understanding of basic principles of statistical inference, including such concepts as bias, sampling distributions, standard errors, confidence intervals, and hypothesis testing. You should also have a good working knowledge of the principles and practice of linear regression. 

It is desirable, but not essential, to have previous training in either longitudinal data analysis, structural equation modeling, or both. If you’ve taken Professor Allison’s courses on either of these topics, you should be well prepared. You should also be an experienced user of at least one of the following statistical packages: SAS, Stata, Mplus, or R.


“I would recommend anyone interested in SEM take this course. It is very pedagogical and the pace is neither too fast nor too slow. You will learn a lot, and you will get both a basic and more advanced understanding of SEM.”
  Dennis Andersson, University of Gothenburg

“This was an excellent course covering an important analytical approach to longitudinal data analysis. Dr. Allison is both a pioneer in this method and an excellent teacher. The online format offers a lot of advantages to participants who wish to revisit materials and ask Dr. Allison carefully considered questions. I highly recommend this course.”
  Xiaoquan Zhao, George Mason University

“I studied this course after taking an econometric class. I feel this course really opened another window for me to think about similar things in a different way, which is quite enlightening.”
  Ying Liang, Wuhan University