Study of context-specific independencies through Chain Stratified Graph Models for categorical variables

This work focuses on the study of the relationships among a set of categorical (ordinal) variables under the perspective of marginal, conditional and contextspecific independencies. If the first two are well known, the last one concerns independencies holding only in a subspace of the outcome space. At this aim we take advantage from the well know relationship between the chain graphical models and the marginal log-linear models and we adapted this by considering the context-specific independencies. The resultant graphical model is a so-called ”stratified” graphical model with labeled arcs that can be described by new constraints on marginal loglinear models. An application about the innovation degree of the Italian enterprises is provided.