  The statistical literature discusses different types of Markov properties for
chain graphs that lead to four possible classes of chain graph Markov models.
The different models are rather well understood when the observations are
continuous and multivariate normal, and it is also known that one model class,
referred to as models of LWF (Lauritzen--Wermuth--Frydenberg) or block
concentration type, yields discrete models for categorical data that are
smooth. This paper considers the structural properties of the discrete models
based on the three alternative Markov properties. It is shown by example that
two of the alternative Markov properties can lead to non-smooth models. The
remaining model class, which can be viewed as a discrete version of
multivariate regressions, is proven to comprise only smooth models. The proof
employs a simple change of coordinates that also reveals that the model's
likelihood function is unimodal if the chain components of the graph are
complete sets.
