Longitudinal Data Analysis Using
Structural Equation Modeling

An Online Seminar Taught by
Paul D. Allison, Ph.D.

Read reviews of the in-person version of this seminar

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

This course is currently full. If you would like to be added to the waitlist, please send us an email at ashley@statisticalhorizons.com.

For the past five years, Dr. Paul Allison has been teaching his acclaimed two-day 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. 

Starting March 8, we will be offering this seminar online for the first time. 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. You may submit your work for review by Dr. Allison.  

Each week, there are two assigned articles to read. There is also an online discussion board 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.

reviews of the live version of longitudinal data analysis using sem

“I have worked theoretically with SEM for many years. This course was an eye-opener for me for how flexible and relevant SEM is for modeling.”
  Ulf Henning Olsson, BI Norwegian Business School

“The pacing of the course is one that allows careful absorption of the material without ever feeling rushed. I enjoyed the exercises at the end of specific sections; the exercises did a great job of continuing with the examples displayed while adding an additional layer of complexity that allows interactive thinking. I also appreciated the implementation/presentation on the various statistical software packages available to move one’s work forward.”
  Carlos Carballo, Henry M. Jackson Foundation

“An amazing course! It builds on existing knowledge in SEM and longitudinal data analysis to create a completely new method that flexibly allows for missing data, reverse causality, and estimating time-invariant parameters. Amazing!”
  Abby Palmer Molina, University of Southern California

“Dr. Allison’s approach to teaching SEM is clear and efficient. The course makes SEM approachable by building on the fundamentals. I feel confident in my ability to use the methods and approaches learned during the course in my work moving forward.”
  Jessica Sanders, University of Utah

“Dr. Allison is a spectacular teacher! He obviously has years of experience with teaching because he organizes his slides well, knows the material inside and out, is very patient and responds to questions very well, and can judge the optimal pace of the class. I found the preparatory materials (recommended articles and slides) extremely helpful to review before the class began. I would highly recommend this class to other colleagues, especially those with a background in SEM.”  
   Mary M. Mitchel, Johns Hopkins University

 “This course completely changed my thinking about how to analyze panel data. SEM offers so much more flexibility than conventional methods and allows one to address, and in some cases overcome, the limitation of such methods.”
  Bill Carbonaro, University of Notre Dame

 “The course made me learn a lot more about SEM and to look at the possible problems I might encounter during the analysis. Professor Paul Allison is very clear on his lecture, and even with little background in SEM, I can say I learned a lot.”
  Ruben Ladwig

“I really appreciate the state-of-the-art insight shown by Paul Allison. Even as an only moderately experienced SEM user, I could follow well. The methods taught are very powerful for strategy/organization behavior studies.”
  Sebastian Fourné, WHU – Otto Beisheim School of Management

 “This course provided a better explanation of fixed versus random effects and showed how they are hidden within procedures like PROC GLM.  It gives many examples of reciprocal causation for different number of time points, lending to a better appreciation of the limitation of having fewer waves of data.”
  Andy Kin On Wong, McMaster University & University Health Network

 “This course provided an excellent discussion of how to apply different SEM models to panel data. It pulled from the latest publication on these topics and provided a framework to analyze my personal data. I was greatly appreciative of learning not just how to code with SEM, by the advantages and tools each software package offered.”
  Elizabeth Hecht, North Carolina State University

“Just took SEM class with Dr. Allison. I knew nothing about SEM but his care of presentation and expertise enabled this complete novice to at least understand the basics behind such a complicated analytical method. Dr. Allison really knows his stuff. Well done. Highly recommend this course and this instructor.”
  Francis Pike, University of Pittsburgh

 “This class is wonderfully paced and helpful in reviewing and background concepts of SEM and also touches on very in-depth concepts as well. The assignments are accessible and helpful in solidifying understanding of core material. The examples provided are thorough enough that I think I could easily use them with my own projects.”
  Tarana Khan, University of California

 “This course gave me a better understanding of SEM in general, as well as exposure to statistical packages I have not previously used. I not only have a better understanding of SEM, but also a firmer grasp of the differences between the statistical package that I use (SAS), vs. other statistical packages. I look forward to applying the techniques I have learned in packages I was previously unfamiliar working with.”
  LaRita Jones, University of Alabama

 “The course material is well-presented and the applied focus of the teaching allows one to readily grasp and apply the relatively complex content/models being covered. The course has certainly introduced tremendous potential in my work with panel-data as an applied statistician.”
  Paul Agius, MacFarlane Burnet Medical Research Institute

“A great, clear introduction to a complex model capable of handling a wide variety of longitudinal designs while requiring very few assumptions about the data. Any researcher who regularly uses fixed effects or random-effects should take the course to see what they are missing.”
  Andy Lin, University of California