Longitudinal Data Analysis Using SEM

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

Read reviews of this course 

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: In typical situations, the use of Arellano-Bond instead of ML-SEM is equivalent to throwing away half the data. 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 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. 

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.

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.


The class will meet on Friday, October 16 and Saturday, October 17 from 9 to 5 each day with a 1-hour lunch break at the Manhattan Beach Marriott, 1400 Parkview Ave, Manhattan Beach, CA 90266.

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 later) 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 includes all course materials. 

Lodging Reservation Instructions

A block of guest rooms has been reserved at the Manhattan Beach Marriott, 1400 Parkview Ave, Manhattan Beach, CA at a special rate of $169 per night. In order to make a reservation, use this link or call 800-266-9432 and identify yourself with Statistical Horizons. The room block will expire when it is full or on Friday, September 25, 2015.


  • 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


“Dr. Allison is a spectacular teacher! He obviously has years of experience with teaching because he organizes his slides well, knows the material inside and out, is very patient and responds to questions very well, and can judge the optimal pace of the class. I found the preparatory materials (recommended articles and slides) extremely helpful to review before the class began. I would highly recommend this class to other colleagues, especially those with a background in SEM.”
  Mary M. Mitchel, Johns Hopkins University 

“This course provided an excellent discussion of how to apply different SEM models to panel data. It pulled from the latest publications on these topics and provided a framework to analyze my personal data. I was greatly appreciative of learning not just how to code with SEM, but the advantages and tools each software package offered.”
  Elizabeth Hecht, North Carolina State University 

“This course completely changed my thinking about how to analyze panel data. SEM offers so much more flexibility than conventional methods and allows one to address, and in some cases overcome, the limitation of such methods.”
  Bill Carbonaro, University of Notre Dame 

“This course provides detailed instructions on the implementation of a modern approach to data analysis, with a discussion of common pitfalls and plenty of opportunity for questions.”
  Greg Pavela, The University of Alabama at Birmingham

“This is a timely course on how to use LDA in the context of SEM.”
  Mahour Parast, North Carolina Agriculture & Technical State University

“I really appreciate the state-of-the-art insight shown by Paul Allison. The methods taught are very powerful for strategy/organization behavior studies.”
  Sebastian Fourné, WHU – Otto Beisheim School of Management 

“This course provided a better explanation of fixed versus random effects and shows how they are hidden within procedures like PROC GLM. It gives many examples of reciprocal causation for different number of time points, lending to a better appreciation of the limitation of having fewer waves of data. This is a good segue into growth curve modeling.”
  Andy Kin On Wong, McMaster University & University Health Network