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.

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.

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 the Holiday Inn Fort Myers Airport at Town Center9931 Interstate Commerce Drive, Fort Myers, FL 33913. This hotel is 5 miles from the Fort Myers International Airport, and there is a complimentary hotel shuttle to and from the airport. The shuttle can also take you to and from the nearby Gulf Coast Town Center, a large open-air shopping center with numerous stores, restaurants, and a movie theater.

Although you can expect the weather to be comfortably warm (75 is the average high in early February), this is not a resort-type location. However, it’s about a half-hour drive to several attractive vacation areas, including Naples, Sanibel Island, and Fort Myers Beach.

The Fort Myers International Airport (RSW) is served by numerous airlines with direct flights to and from most major cities in the U.S. However, demand for seats in February is quite high, so be sure to make reservations at your earliest opportunity.

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 course materials.

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 Holiday Inn Fort Myers Airport at Town Center, 9931 Interstate Commerce Drive, Fort Myers, FL 33913 at a special rate of $169. In order to make reservations, call 239-561-1550 during business hours and identify yourself as part of the Statistical Horizons Meeting, or click here. For guaranteed rate and availability, you must reserve your room no later than Friday, December 28, 2018.

We also recommend going directly to the hotel’s website or checking other online hotel sites. Pricing varies and you may be able to secure a better rate. 


  • 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


“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

“The course (Longitudinal Data Analysis Using SEM) was a great review of models in Stata, SAS, Mplus, and R. Highly recommend the course for people interested in the methodology.”