  Depending on the interpretation of the type of edges, a chain graph can
represent different relations between variables and thereby independence
models. Three interpretations, known by the acronyms LWF, MVR, and AMP, are
prevalent. Multivariate regression chain graphs (MVR CGs) were introduced by
Cox and Wermuth in 1993. We review Markov properties for MVR chain graphs and
propose an alternative global and local Markov property for them. Except for
pairwise Markov properties, we show that for MVR chain graphs all Markov
properties in the literature are equivalent for semi-graphoids. We derive a new
factorization formula for MVR chain graphs which is more explicit than and
different from the proposed factorizations for MVR chain graphs in the
literature. Finally, we provide a summary table comparing different features of
LWF, AMP, and MVR chain graphs.
