Binary models of marginal independence: a comparison of different approaches

This work compares the performances of three parameterizations for defining parsimonious submodels of binary bidirected graph models. In particular, it shows that the log-mean linear parameterization, recently developed by Roverato, Lupparelli and La Rocca (2012) provides a useful tool to include in the model additional linear constraints with a clear interpretation in terms of independencies in special subpopulations. The features of the three parameterizations are illustrated through an example based on a data set with seven binary variables