Suppose that loglinear model (XY, XZ) holds. a. Find and log ij+ . Show the loglinear model for the XY marginal table has the

Suppose that loglinear model (XY, XZ) holds.

a. Find and log µ_ij+. Show the loglinear model for the XY marginal table has the same association parameters as {λ_ij^XY} in (XY, XZ). Deduce that odds ratios are the same in the XY marginal table as in the partial tables. Using an analogous result for model (XY, YZ), deduce the collapsibility conditions in Section 9.1.2.

b. Calculate log µ_ij+ for model (XY, XZ, YZ), and explain why marginal associations need not equal conditional associations.