Title: Old and New Approaches for Analyzing Categorical Data in a SEM
Framework

Author: Yves Rosseel

Abstract: In traditional software for structural equation modeling (SEM),
there are two options to deal with binary and ordinal observed variables. The
first option is called the three-stage limited information approach (in the
Mplus world, this known as estimator WLSMV). The second option is based on the
IRT tradition where full information maximum likelihood estimation is the
golden standard. Recently, a new approach called pairwise maximum likelihood
(PML) has been introduced in the literature. This approach uses bivariate
information only, making it computationally feasible to handle large models
with many observed and latent variables (unlike full ML). But PML is still
rooted in the (composite) maximum likelihood framework (unlike WLSMV) and
inherits many of its desirable statistical properties.

In this talk, I will briefly discuss the three approaches, and their
implementation in SEM software. The PML approach is currently only implemented
in the R package lavaan, and serves as an example of how open-source software
can foster the development of new statistical ideas.