In the situation of Problem 14.65, 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

ˆpi j =

Yi j /(1 + λi − λj), where the λ’s are the solutions of the equations j Yi j /(1 +

λi − λj) =

j Yi j /(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.