In this work we handle with categorical (ordinal) variables and we focus on
the (in)dependence relationship under the marginal, conditional and
context-specific perspective. If the first two are well known, the last one
concerns independencies holding only in a subspace of the outcome space. We
take advantage from the Hierarchical Multinomial Marginal models and provide
several original results about the representation of context-specific
independencies through these models. By considering the graphical aspect, we
take advantage from the chain graphical models. The resultant graphical model
is a so-called "stratified" chain graphical model with labelled arcs. New
Markov properties are provided. Furthermore, we consider the graphical models
under the regression poit of view. Here we provide simplification of the
regression parameters due to the context-specific independencies. Finally, an
application about the innovation degree of the Italian enterprises is provided.Comment: 21 pages, 4 tables, 3 figure
