Context-specific independencies for ordinal variables in chain regression models

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.