Longitudinal Data Analysis Using Structural Equation Modeling

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

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For the past eight 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. You are strongly encouraged to bring your own data and try out the new methods. 

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.


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 and Materials 

The course meets 9 a.m. to 5 p.m. on Thursday, October 6 and Friday, October 7 at the University of Limerick, Limerick, Ireland.  For travel information and directions, click here.

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 €895 covers all course materials.

Lodging Reservation Instructions

Kilmurry Lodge Hotel, Dublin Road, Limerick, Ireland. A block of rooms has been reserved at a rate of €79.00 per night for a Single or €94.00 per night for a Twin/Double. Contact the hotel directly at 061-331133 Ext 1 or email info@kilmurrylodge.com.  Please reserve before the rate expires on September 4 and quote reservation number 231615 and ‘Statistical Horizons LCC’ in order to receive the discount rate.

Castleroy Park Hotel, Dublin Road, Castletroy, Limerick. A block of rooms has been reserved at a rate of €90.00 per night for a Single or €100.00 per night for a Twin/Double. Contact the hotel directly by calling 0035361335566 (Ext 1 for Reservations) or emailing reservations@castletroypark.ie. Please reserve before the rate expires on September 7 and mention the Hotel Reference number 201689 and Statistical Horizons LLC.

Seminar outline

  • 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
  • Linear and quadratic effects of time.
  • Missing data by FIML
  • Random coefficients
  • Higher-level clustering
  • Alternative estimators
  • Other latent variables
  • Categorical outcomes

Comments from recent participants

“This is a very informative, intense course on a novel approach to combine fixed effects model with cross-lagged model using SEM approach. I truly appreciate that Dr. Allison provides information in a very organized way that helps me to understand difficult concepts more easily.”
  Hye Won Kwon, University of Iowa

“As a graduate student, this course was extremely helpful. I learned more in 2 days than 2 semesters of the same statistics courses. Dr. Allison is very knowledgeable and presents complex material beautifully and clearly.”
  Daniel Paulus, University of Houston

“The best course about causal inference, reverse causation and unmeasured confounding!”
  Hyun Joon Shin, Harvard Medical School

“This class includes an emphasis on coding that I found extremely practical. I appreciate that Paul’s materials included coding examples from several software packages, while lectures focused on a couple in the interest of time. Further, the provided materials will surely be a great resource after the class, they are clear and detailed.”
  Sarah Spell, The Pew Charitable Trust