Consider the cumulative logit model, logit[P(yi ≤ j)] = ????j + ????jxi.

a. With continuous xi taking values over the real line, show that the model is improper, in that cumulative probabilities are misordered for a range of xi values.

b. When xi is a binary indicator, explain why the model is proper but requires constraints on (????j + ????j) (as well as the usual ordering constraint on {????j})

and is then equivalent to the saturated model.