Suppose that { ijk } in a 2 2 2 table are, by row, (0.15, 0.10 / 0.10, 0.15) when Z = 1

Suppose that {π_ijk} in a 2 × 2 × 2 table are, by row, (0.15, 0.10 / 0.10, 0.15) when Z = 1 and (0.10, 0.15 / 0.15, 0.10) when Z = 2. For testing conditional XY independence with Logit models having Y as a response, explain why the Likelihood-ratio test comparing models X + Z and Z is not consistent but the likelihood-ratio test of fit of the XY conditional independence model is.