Categorical Structural Equation Modeling

A 3-Day Remote Seminar Taught by
Kevin Grimm, Ph.D.

Read reviews of this course

To see a sample of the course materials, click here.

Structural equation modeling (SEM) is a framework for fitting many types of statistical models, including simple regression models, multivariate path models, confirmatory factor models, latent variable path models, and latent growth models. Since its inception, the standard SEM has been a linear model with normally distributed outcomes. That’s been a big limitation because many outcome variables are binary or ordinal in almost every discipline.  

While many SEM packages are still limited to linear/normal models, the last decade has seen the emergence of several SEM packages that do an excellent job of estimating non-normal models. Unfortunately, these models differ in several ways from standard SEM, and there is little didactic literature on how to properly use and interpret categorical SEM. 

This seminar fills that gap by presenting a comprehensive treatment of SEM for binary and ordinal outcomes, using two of the best software packages for the task: Mplus and lavaan (a package for R).  

Starting November 4, we are offering this seminar as a 3-day synchronous*, remote workshop. Each day will consist of a 4-hour live lecture held via the free video-conferencing software Zoom. You are encouraged to join the lecture live, but will have the opportunity to view the recorded session later in the day if you are unable to attend at the scheduled time.

Each lecture session will conclude with a hands-on exercise reviewing the content covered, to be completed on your own. An additional lab session will be held Thursday and Friday afternoons, where you can review the exercise results with the instructor and ask any questions.

*We understand that scheduling is difficult during this unpredictable time. If you prefer, you may take all or part of the course asynchronously. The video recordings will be made available within 24 hours of each session and will be accessible for four weeks after the seminar, meaning that you will get all of the class content and discussions even if you cannot participate synchronously.

Closed captioning is available for all live and recorded sessions.


The following statistical models will be discussed:

  • Logistic and probit regression and path models
  • Cumulative logit and probit regression and path models
  • Confirmatory factor models for binary and ordinal indicators (e.g., 2-parameter logistic model, graded response model)
  • Multiple group confirmatory factor models for binary and ordinal indicators
  • Count outcomes in structural equation models


This seminar will use R and Mplus for the empirical examples and exercises. To participate in the hands-on exercises, you should have a computer with Mplus and R installed. You should also install RStudio, a freely available interface for R, and the lavaan package for SEM. 

If you’d like to take this course but are concerned that you don’t know enough R, there are excellent on-line resources for learning the basics. Here are our recommendations.

WHO SHOULD Register? 

If you want to learn how to apply structural equation models to binary and ordinal data and have a solid background in structural equation modeling, then this course is for you. Familiarity with either R or Mplus is strongly advised.


Day 1: Path Analysis with Binary Outcomes

  • Introduction to structural equation modeling
  • Review of logistic and probit regression in R
  • Introduction to Mplus and lavaan notation
  • Logistic and probit regression in Mplus and lavaan
  • Maximum likelihood estimation and weighted least squares estimation
  • Path models with binary mediators and outcomes

Day 2: Ordinal Outcomes & Confirmatory Factor Models

  • Cumulative logit and probit regression models in R
  • Cumulative logit and probit regression models in Mplus and lavaan
  • Model fit for maximum likelihood and weighted least squares estimators
  • Confirmatory factor models with binary indicators
  • Confirmatory factor models with ordinal indicators
  • Latent variable path models with binary and ordinal indicators

Day 3: Multiple Group Confirmatory Factor Analysis, Missing Data, & Count Outcomes

  • Multiple group confirmatory factor analysis with binary and ordinal indicators
  • Missing data handling with maximum likelihood and weighted least squares estimators
  • Review of count regression models in R
  • Count regression models in Mplus
  • Zero-inflated count regression models in Mplus

REVIEWS OF Categorical Structural Equation Modeling

“It was an excellent course with deep topic coverage. I liked that Prof. Grimm explained topics clearly and broadly linked them to other statistical approaches (e.g. linkage between SEM and IRT). I also liked that codes were explained in two broadly used softwares: MPlus and the lavaan package for R, and advantages of each one were clearly compared.”
  David Greger, Charles University, Prague 

“Dr. Grimm is a talented instructor who does a great job of elucidating complicated concepts and clarifying exactly how Mplus and lavaan produce their estimation results. This seminar provides an accessible guide to applying a variety of techniques which I was able to put to immediate use in my work.”
  Julien Leider, University of Illinois Chicago