A cumulative link model for an I J contingency table with a qualitative predictor is G
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A cumulative link model for an I × J contingency table with a qualitative predictor is G–1[P(Y ≤ j)] = αj + µi, 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 = ... = µI and the test of independence has df = I – 1.
c. When this model holds, show that the rows are stochastically ordered on Y.
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