Structural Equation Models for Categorical Outcomes Using lavaan

Terrence D. Jorgensen


Full day short course (9:00am – 5:00pm)

Structural equation modeling (SEM) is a very general statistical technique widely used technique in social and behavioral sciences.  Originally developed for normally distributed data, SEM has been adapted for discrete data (e.g., binary checklists, ordinal Likert scales) more commonly employed in psychological research.  Instead of normally distributed observed responses, the standard SEM applies to normally distributed latent responses, which are linked to discrete observations via a threshold model, which is statistically equivalent to using a (cumulative) probit link function in a generalized linear model for discrete responses. 

Similar to common factors, distributions of latent responses do not have known locations or scales, so arbitrary identification constraints are needed to estimate SEM parameters.  This course explains various common identification methods implemented in SEM software, comparing and contrasting these methods using demonstrations on simulated and human-subjects data.  We begin with univariate probit regression within the SEM framework, extending that to path analyses representing hypotheses of mediation.  Item factor analysis is then demonstrated, along with how to obtain model-based reliability estimates using Green & Yang’s (2009) approach from Psychometrika. Given a set of identification constraints, differences in latent-response distributions can be estimated and tested, which I demonstrate in two contexts: estimating latent-growth models and evaluating measurement equivalence/invariance. Data and R syntax is provided for all examples and exercises.

Intended Audience

Researchers and graduate students who conduct simulation studies involving SEM. Basic familiarity with SEM and some experience with R will be assumed. Familiarity with the lavaan package’s model syntax is recommended but not required; an introductory tutorial can be found on the website:

Software Requirements

All instruction and example syntax will utilize the R software.  Attendees with laptops can participate more interactively.  Add-on packages can be installed from CRAN using the R syntax:


About the instructor

Terrence D. Jorgensen

Terrence D. Jorgensen Terrence D. Jorgensen, PhD, teaches SEM as an assistant professor of methods and statistics within the Department of Child Development and Education at the University of Amsterdam.  He maintains the R packages semTools and simsem, coauthors the lavaan package, and contributes to the blavaan package.

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