A cumulative link model for an I J contingency table with a qualitative predictor is G 1 [P(Y j)] = j +

A cumulative link model for an I × J contingency table with a qualitative predictor is G^–1[P(Y ≤ j)] = α_j + µ_i, i = 1,...., I, j = 1,...., J – 1.

a. Show that the residual df = (I – 1)(J – 2).

b. When this model holds, show that independence corresponds to µ₁ = ... = µ_I and the test of independence has df = I – 1.

c. When this model holds, show that the rows are stochastically ordered on Y.