Longitudinal Data Analysis Using Structural Equation Modeling

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

Read reviews of this seminar

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 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 investigate 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. Models that combine these two approaches are .well known to econometricians as dynamic data panel models.

Professor Allison and his colleagues have shown that these kinds of 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 econometric methods with respect to both bias and efficiency. 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 data 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 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 profile 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 data 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 Beacon Hotel, 1615 Rhode Island Ave NW, Washington, D.C. 20036.

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.

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 Beacon Hotel, 1615 Rhode Island Ave NW, Washington, D.C., where the seminar takes place, at a special rate of $259 on October 24 and $179 on October 25. In order to make reservations, call 202-787-1784 during business hours or email emendoza@beaconhotelwdc.com and identify yourself as part of the Statistical Horizons group. For guaranteed rate and availability, you must reserve your room no later than Wednesday, September 25, 2019.

A block of guest rooms has also been reserved at Hotel 1600, 1600 Rhode Island Ave NW, Washington, D.C. at a special rate of $189 per night. This hotel is about a 2-minute walk to the seminar location. In order to make reservations, click here and enter the group code STATISTICALH. Next, click the orange ‘Check Availability’ button on the right to view available rooms. For guaranteed rate and availability, you must reserve your room no later than Thursday, September 26, 2019.


  • Introduction
    • Characteristics of panel data
    • Objectives of panel modeling methods
    • Path Analysis
  • SEM for cross-lagged models
    • 3-wave, 2 variable model
    • SEM software
    • Estimation and assumptions
    • Goodness of fit
    • Equality constraints
  • SEM for fixed effects models
    • Why fixed effects?
    • Classic estimation methods
    • SEM estimation
    • Introduction to xtdpdml (for Stata) and dpm (for R)
    • Time-invariant predictors
  • Combining cross-lagged and fixed effects models
    • Issues with lagged predictors
    • Allowing for reverse causation
    • Missing data via FIML
  • One-sided estimation
  • Extended example
    • Unobservables with time-varying effects
    • Reverse causation
    • Getting the lags right
  • Categorical outcomes
  • Count data outcomes


“The course was well designed and organized. The course description and requirements on the website were helpful in deciding if I was at an appropriate level to understand the lectures and profit from the hands-on exercises. This was easily the only two-day course I have taken where I left feeling confident that I could use a methodology that was new to me but useful for my research.”
  Dhananjay Vaidya, Johns Hopkins University

“Dr. Allison is very knowledgeable and an engaging instructor. This course is a great introduction to longitudinal SEM. You will leave prepared to apply the techniques you learned using a variety of software packages.”
  Rebecca Alper, Temple University

“This is a good course to quickly learn Professor Allison’s work on fixed effects models for longitudinal data and cross lagged longitudinal data model for exploring causal relationships from panel data. The course is well-organized. The handouts contain computer code that make it easy for learners to quickly get a sense of these models and their performances. Professor Allison is a great instructor.”
  Ming Ji, University of South Florida

“This is an interesting class for examining causal relationships in data without having a randomized experimental design.”
  Sue Ferguson, The Ohio State University

“The course was exceptionally well organized with a balance of lecturing and coursework throughout the days. There was a nice heavy emphasis on performing analysis across different statistical platforms with comparison statistics. Notes provided are excellent for further reference.”
  Kristian Lynch, University of South Florida

“Most of the data I work with is longitudinal. I’ve recently started using data collected during screening as proxy items of factors related to future response. This course was very helpful for understanding SEM in longitudinal framework. There were many variables that I hadn’t even considered as being longitudinal prior to taking this class. It was very timely and very informative.”
  Morgan Earp, US Bureau of Labor Statistics

“The instructor’s knowledge of the different tools thereby enabling students to learn disregarding their current tooling was invaluable. The reference to seminal publications was also quite helpful.”

“This course greatly helped me understand how the statistics concepts are applied in the packages.”
  William R. Nichols, Carnegie Mellon University