In the situation of Problem 12.63, consider the hypothesis of marginal homogeneity H
: pi+ = p+i for all i, where pi+ = a j=1 

piij , p+i = a j=1 pjii.

(i) The maximum-likelihood estimates of the piij under H
are given by ˆ
pˆij = Yij/(1+λi−λj ), where the λ’s are the solutions of the equations 
j Yij/(1+
λi−λj ) = 
j Yij/(1+λj−λi). (These equations have no explicit solutions.)
(ii) Determine the number of degrees of freedom for the limiting χ2-distribution of the likelihood ratio criterion.