Marginal parametrizations for conditional independence models and graphical models for categorical data

The graphical models (GM) for categorical data are models useful to representing conditional independencies through graphs. The parametric marginal models for categorical data have useful properties for the asymptotic theory. This work is focused on nding which GMs can be represented by marginal parametrizations. Following theorem 1 of Bergsma, Rudas and Németh [9], we have proposed a method to identify when a GM is parametrizable according to a marginal model. We have applied this method to the four types of GMs for chain graphs, summarized by Drton [22]. In particular, with regard to the so-called GM of type II and GM of type III, we have found the subclasses of these models which are parametrizable with marginal models, and therefore they are smooth. About the so-called GM of type I and GM of type IV, in the literature it is known that these models are smooth and we have provided new proof of this result. Finally we have applied the mean results concerning the GM of type II on the EVS data-set.