9.4 For a 22 contingency table, the maximal log-linear model can be written as 11 =

9.4 For a 2×2 contingency table, the maximal log-linear model can be written as

η11 = µ +α +β + (αβ), η12 = µ +α −β −(αβ),

η21 = µ −α +β −(αβ), η22 = µ −α −β + (αβ), where ηjk = logE(Yjk) = log(nθ jk) and n = ∑∑Yjk.

Show that the interaction term (αβ) is given by

(αβ) = 1 4

logφ, where φ is the odds ratio (θ11θ22)/(θ12θ21), and hence that φ = 1 corresponds to no interaction.