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8.37 Consider the cumulative logit model, logit[ P(Y < j)] = Î±j Î²jx, not having proportional odds form. With continuous x taking values over the real line, show that the model is improper in that cumulative probabilities are misordered for a range of x values. When X is a binary indicator, explain why the model is proper but requires constraints on (Î±j Î²j) (as well as the usual ordering constraint on Î±j) and is then equivalent to the saturated model.

8.37 Consider the cumulative logit model, logit[ P(Y < j)] = Î±j Î²jx, not having proportional odds form. With continuous x taking values over the real line, show that the model is

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