Graphical models for three dimensional contingency tables with symmetries

The class of graphical log-linear models for homologous factors introduced by Gottard (2009), called Symmetric-Quasi-Symmetric graphical models, is analyzed in this paper. The conditional independence structure of a SQS model is represented by a coloured graph in which constraints on main effects are associated with coloured nodes and constraints on interaction parameters are associated with coloured edges. Limiting to the case of three dimensional tables, all possible configuration of symmetric tables and margins are here investigated.