Longitudinal Data Analysis Using Structural Equation Modeling

A 2-Day Seminar taught by Paul D. Allison, Ph.D. 

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

For the past ten years, Professor Paul Allison has been teaching his acclaimed two-day seminars on Longitudinal Data Analysis Using SAS and Longitudinal Data Analysis Using Stata. In this new seminar he takes up where those courses leave off, with methods for analyzing panel data using software for structural equation modeling (SEM).

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 has recently shown that dynamic panel models can easily be estimated by maximum likelihood with SEM software (ML-SEM). His recent 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 at least two hours of carefully-designed and supervised exercises using real data.

Mplus will be the main software package used in this course. However, program code for three other packages will also be included in the slides: SAS, Stata, and the new lavaan package for R. The exercises can be done with any of these 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 will be included in the slide deck. To participate in the hands-on exercises, you are strongly encouraged to bring a laptop computer with one of these packages installed.  

Who should attend? 

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.

Location, Format, AND Materials 

The class will meet from 9 am to 5 pm each day with a 1-hour lunch break at Jamaica Bay Inn, 4175 Admiralty Way, Marina Del Rey, CA 90292. 

Participants receive a bound manual containing detailed lecture notes (with equations and graphics), examples of computer printout, and many other useful features. This book frees participants from the distracting task of note taking. 

Registration and lodging

The fee of $995.00 includes all seminar materials. The early registration fee of $895 is available until April 17.

Refund Policy

If you cancel your registration at least two weeks before the course is scheduled to begin, you are entitled to a full refund (minus a processing fee of $50). 

Lodging Reservation Instructions

A block of guest rooms has been reserved at the Jamaica Bay Inn, 4175 Admiralty Way, Marina Del Rey, CA 90292, where the seminar takes place, at a special rate of $209-$229 per night. In order to make reservations, call 310-823-5333 during business hours and identify yourself as part of the Statistical Horizons group. For guaranteed rate and availability, you must reserve your room no later than Monday, April 16, 2018. 


  • Characteristics of panel data
  • Objectives of panel modeling methods
  • Review
    • Random effects models
    • Fixed effects models
    • Cross-lagged panel models
    • SEM modeling
  • Problems
    • Dependence among repeated measures
    • Lagged dependent variables
    • Problems with reciprocal causation
  • Difference scores for T=3
  • Econometric solutions
    • Arellano-Bond
    • System estimator
    • ML methods
  • SEM for random effects
  • SEM for fixed effects
  • SEM with lagged endogenous and predetermined variables.
  • SEM compared with Arellano-Bond
  • SEM details
    • Evaluating model fit.
    • Relaxing constraints
    • Higher-order lags
    • Likelihood ratio tests
    • Allowing coefficients to vary with time
  • Missing data by FIML
  • Random coefficients
  • Higher-level clustering
  • Alternative estimators
  • Other latent variables
  • Categorical outcomes


“Dr. Allison is well-versed in the material, which is enough to come to the workshop. But, I also find him very patient and kind. I wish I could add him to my dissertation committee!”
  Brennan Rhodes-Bratton, Columbia University

“I was well-versed in longitudinal data analysis before taking this course, but had very little knowledge of SEM. This was a great 2-day crash course. The example data sets provided were very helpful. I liked being able to follow along on my own computer throughout the course. The exercises also helped solidify the concepts we were taught. I appreciate that Dr. Allison demonstrated how to fit these models in multiple software packages. Thank you!”
  Melissa Braschel, Gender & Sexual Health Initiative, BC Centre for Excellence in HIV/AIDS

“This intensive course is an excellent way for researchers to do continuing education on methods that address current needs from the availability of longitudinal data. The course is taught by one of the best experts in this area, who also masters great pedagogical skills!”
  Kare Sandvik, University College of Southeast Norway

“A comprehensive course in only 2-days! The instructor was knowledgeable, clear, and answered questions effectively and efficiently.”
  Meghan Schreck, Brown University, Warren Alpert Medical School

“I really enjoyed the applied nature of the course and the use of real world examples. Providing code for multiple statistical packages was very useful. There were plenty of opportunities to ask questions. Paul is an excellent educator. I would very much recommend this course to individuals with an intermediate or higher statistical skill-set/knowledge base.”
  Jackie White Hughto, Yale University

“Really enjoyed Dr. Allison’s lecture. Great examples, clear explanations and new skills and methods.”

“This is a course that demands the attention of the student and the active engagement of the student in learning. However, the techniques described in the course are of enormous assistance in considering how to appropriately model and analyze panel data using SEM.”
  Janette Baird, Brown University, Warren Alpert School of Medicine

“A wonderful course. The materials include the codes and examples for four different types of software. Also, very helpful for future reference.”
  Ji Li, University of Oklahoma Health Sciences Center

“I thought this was a great class – well-organized and coherent. The instructor is very good and respectful of questions. Looking forward to taking others!”
  Ann Miller, Harvard Medical School

“This course offered a novel and compelling alternative to traditional auto-regressive cross lagged models for testing causal effects using correlational longitudinal data.”
  Sam Hardy, Brigham Young University