8.37 Consider the cumulative logit model, logit[ P(Y < j)] = αj βjx, 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 (αj βj) (as well as the usual ordering constraint on αj) and is then equivalent to the saturated model.
8.37 Consider the cumulative logit model, logit[ P(Y < j)] = αj βjx, not …
Dec 28, 2022
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