Consider model (AC, AM, CM, AG, AR, GM, GR) for the drug use data in Section 7.4.5.
a. Explain why the AM conditional odds ratio is unchanged by collapsing over race, but it is not unchanged by collapsing over gender.
b. Suppose we remove the GM term. Construct the independence graph, and show that {G, R} are separated from {C,M} by A.
c. For the model in (b), explain why all conditional associations among A, C, and M are identical to those in model (AC, AM, CM), collapsing over G and R.