Context-specific independence in innovation study

This chapter focuses on the so-called context-specific (CS) independence where the conditional independence holds only in a subspace of the outcome space. The main aspects concern the definition in the same model of marginal, conditional and CS independencies, through the marginal models. The chapter investigates how it is possible to test these CS independencies when there are ordinal variables. Finally, it proposes a graphical representation of all the considered independencies taking advantages from the chain graph model (CGM) and shows the results of an application on "The Italian Innovation Survey". Trivially, the CGMs are graphical models that take advantages from chain graphs to describe a system of independencies. CGMs are used when the variables to analyze are of a different nature, such that they can be naturally collected in different components.