Consider the loglinear model for a four-way table having AB, AC, and AD two-factor terms and no three-factor interaction term. What is the impact of collapsing over B on the other associations? Contrast that with what the collapsibility condition in Section 7.2.7 suggests, treating group S3 = {B}, (i)

if S1 = {C} and S2 = {A,C}, (ii) if S1 = {C, D} and S2 = {A}. This shows that different groupings for that condition can give different information.