8 37 Consider The Cumulative Logit Model Logit P Y A Bjx Not Having Pro Portional Odds Form A With Conti 1 (59.63 KiB) Viewed 40 times
8.37 Consider the cumulative logit model, logit[P(Y < ] = a; + Bjx, not having pro- portional odds form. a. 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. b. When x is a binary indicator, explain why the model is proper but requires constraints on (a; +B;) (as well as the usual ordering constraint on {a;}) and is then equivalent to the saturated model.
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] = a; + Bjx, not having pro- portional odds form. a. 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. b. When x is a binary indicator, explain why the model is proper but requires constraints on (a; +B;) (as well as the usual ordering constraint on {a;}) and is then equivalent to the saturated model.