Consider the loglinear model with symbol (XZ, YZ). a. For fixed k, show that { ijk } equal the fitted values for testing independence between

Consider the loglinear model with symbol (XZ, YZ).

a. For fixed k, show that {µ̂_ijk} equal the fitted values for testing independence between X and Y within level k of Z.

b. Show that the Pearson and likelihood-ratio statistics for testing this model’s fit have form X² = ∑X²_k, where X²_k, tests independence between X and Y at level k of Z.