The study of (in)dependence relationships among a set of categorical variables collected in a contingency table is an amply topic. In this work we want to focus on the so called context-specific independence where the conditional independence holds only in a subspace of the outcome space. The main aspects that we introduce concern the definition in the same model of marginal, conditional and context-specific independencies, through the marginal models. Furthermore, we investigate how it is possible to test these context-specific independencies when there are ordinal variables. Finally, we propose a graphical representation of all the considered independencies taking advantages from the chain graph model. We show the results on an application on \u201dThe Italian Innovation Survey\u201d of Istat (2012)
