Longitudinal Data Analysis Using SEM

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

Read reviews of Dr. Allison’s previous courses 

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—offered for the first time in January 2015—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. In this seminar, we’ll explain the Arellano-Bond method and its close relatives, and we’ll see how to implement them in both SAS and Stata.

However, Arellano-Bond is known to be statistically inefficient and can also be severely biased in important situations. By contrast, 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 vastly superior to the econometric methods: In typical situations, the use of Arellano-Bond instead of ML-SEM is equivalent to throwing away half the data. Plus, ML-SEM offers superior 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 three 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. There will also be opportunities to consult with Professor Allison on your own longitudinal research projects.

Four different software packages will be used to demonstrate the methods: Mplus, SAS, Stata and the new lavaan package for R. Program code for all four packages will be presented for each example, whenever possible.  

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. In fact, we guarantee it (see below).

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.

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.

Enrollment in this seminar is strictly limited to 25 people.


The class will meet from 9 am to 5 pm each day with a 1-hour lunch break at Courtyard Fort Myers at Gulf Coast Town Center, 10050 Gulf Center Drive, Fort Myers, Florida 33913.

This hotel is part of a large shopping center with numerous stores, restaurants, and a movie theater. It’s 3 miles from the Fort Myers International Airport, and there is a complementary hotel shuttle to and from the airport. Although you can expect the weather to be comfortably warm (75 is the average high in January), this is definitely 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 January 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. 


This seminar is designed as a hands-on course, so you should definitely bring your laptop with one of the following packages installed: Mplus (version 7.1 or later), SAS (version 9.2 or later), Stata (version 12 or 13) or R (with the lavaan package installed). Power outlets and Wi-Fi will be provided.

If you plan to bring your own data, it’s best to bring it in both the wide form (one record per individual) and the long form (multiple records per individual). SEM estimation of dynamic panel models requires that the data be in the wide form. It’s especially important for R users to bring data in the wide form because it can be cumbersome to convert from one form to the other in that package. 

Also for R users: Because Professor Allison’s experience with R is not extensive, his ability to provide detailed help and consultation for analysis using R may be limited.

Registration and lodging

The fee of $995.00 includes all seminar materials. The early registration fee of $895 is available until January 1.

Lodging Reservation Instructions

A block of guest rooms has been reserved at the Courtyard Fort Myers at Gulf Coast Town Center, 10050 Gulf Center Drive, Fort Myers, Florida 33913 at a special rate of $189 per night. In order to make reservations, call 239-332-4747 during business hours and identify yourself by using group name Statistical Horizons. The room block will expire when it is full or on Wednesday, December 24, 2015. 


We are so confident that this course will meet or exceed your expectations, that we guarantee it. If you are not completely satisfied, just let us know and your course fee will be promptly refunded. But please see the cautions above about course content, and make sure that you meet the prerequisites before registering.


  • 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



“This course was a clear, comprehensive and well organized introduction to SEM. Unlike other courses that say no prior SEM knowledge needed, for this one it is actually true!! The instructor, Paul Allison, makes the material so accessible that you go from zero to hero quickly.”
  April Taylor, California State University

“This course is comprehensive in that it covers a lot of the materials you are likely to encounter in working with SEM. Dr. Allison is a very good instructor – slow paced and receptive to questions throughout the course. Overall, though, it’s an excellent exposé on the topic. Thank you Dr. Allison!”
  Karabi Nandy, UCLA 

“Coverage of complex material was clear and well-paced. Dr. Allison’s expertise across a variety of SEM packages is impressive, making the course accessible to a wide range of researchers.”
  Paul Glavin, McMaster University

“What a pleasure it is to learn from Paul Allison! The entire course was logically-sequenced and filled with examples that I can apply in my teaching and research. Best of all, the examples improved my understanding of the advantages and disadvantages of the alternative approaches. Thank you for sharing your expertise!”
  Robert Nielsen, University of Georgia

“This was one of the most useful classes I have attended. I gained a much better understanding of all the ins and outs of longitudinal data analysis as well as practical issues. These are things you cannot get from a textbook.”
  Carolyn Coburn, Stonybrook 

“This course was extremely helpful for me to understand the differences between random effects and fixed effects models. Having real data sets to analyze, as well as the practical approach of the course, I’d say are its main features. The course is very well organized and gives a clear and concise comparison of the different methods available for panel data analysis. Thank you, Dr. Allison, for this magnificent course.”
  Paula Sanchez-Romeu, Banco de Mexico