Graphical Model of type II: a smooth subclass

The Probabilistic Graphical Models (GM) use graphs for representing the joint distribution of q variables. These models are useful for their ability to capture and represent the system of independences relation- ships between the variables involved, even when this is complex. This work concerns categorical variables and the possibility to represent sym- metric and asymmetric dependences among categorical variables. At this aim we introduce the Chain Graphical Models proposed by Andersson, Madigan and Perlman (2001), also known as Chain Graphical Models of type II (GMs II). The GMs II allow for symmetric relationships typical of log-linear model and, at the same time, asymmetric dependences typ- ical Graphical Models for Directed acyclic Graph. In general GMs II are not smooth, however this work provides a subclass of smooth GMs II by parameterizing the probability function through marginal log-linear mod- els. Furthermore, we apply the proposed model to a data-set from the European Value Study (EVS), 2008.