Question: what is the relationship between marginal homogeneity and symmetry?
Answer: Symmetry has two components: marginal homogeneity & quasi-symmetry. Symmetry is a special case of quasi-symmetry. If the quasi-symmetry relationship/model holds, then a way to test for marginal homogeneity is: G2(marginal homogeneity) = G2(symmetry) − G2(quasi-symmetry) with df = I −1.