Jacques A. Hagenaars
Causal Models for Categorical Data

Applying principles from loglinear modeling, latent class analysis
and graphical modeling an integrated approach for the analysis of
categorical data can be formulated. This approach is in the Yulean
tradition where categorical variables are treated as truly categorical
and not as, in the Pearsonian tradition, where categorical data are
just realizations of underlying continuous variables.
As in the 'standard' structural equation modeling, a system of
equations has to be defined for a set of causally ordered variables.
The variables may be of different measurement levels. Further
latent variables may be introduced to take all kinds of systematic
and unsysematic measurement errors and misclassifications into
account.