The proportional odds assumption: Using a cumulative model, define the odds of being at a particular point on the scale or lower as P(y ≤ j|x)

1−P(y ≤ j|x)

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The “proportional odds” assumption derives from the fact that, when the assumption is employed, the odds ratio associated with two values of x (say, x1 and x2) does not depend on j. Show that this holds for cumulative models.