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Consider a 2 ×K contingency table (Table 9.14 ) in which the column totals y. k are fixed for k=1, …, K (a) Show that the product multinomial distribution for this table reduces to f(z1, …, zK / n1, …, nK)=∑k=1^K( nk zk) πk^zk(1-πk)^nk-zk where nk=y-k, zk=y1 k, nk-zk=y2 k, πk=θ1 k and 1-πk=θ2 k, for k=1, …, K . This is the product binomial distribution and is the joint distribution for Table 7.1 (with appropriate changes in notation). (b) Show that the log-linear model with η1 k=logE(Zk)=
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