Refer to logit model (6.4) for a 2 × 2 × K contingency table {n_ijk}.

a. Using dummy variables, write the log-likelihood function. Identify the sufficient statistics for the various parameters. Explain how to conduct exact conditional inference about the effect of X, controlling for Z.

b. Using a basic result for testing in exponential families, explain why uniformly most powerful unbiased tests of conditional XY independence are based on ∑_k n_11k.