Consider the model log(mijk) = u + u1(i) + u2(j) + u3(k) + u12(ij). (a) Show that

Question:

Consider the model log(mijk) = u + u1(i) + u2(j) +

u3(k) + u12(ij).

(a) Show that the maximum likelihood estimate of u3(1) − u3(2) is log(n··1) − log(n··2).

(b) Show that maximum likelihood estimation gives log

uˆ12(11)uˆ12(22)

uˆ12(12)uˆ12(21)

= log(n11·) − log(n12·) − log(n21·) + log(n22·).

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Shameen Tahir

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