Suppose that in a certain multinomial logistic regression there are three events

Question

Suppose that in a certain multinomial logistic regression there are three events 1, 2 and 3. Suppose there are two situations A and B. For situation A the probability of event 1 is 0.2, that of event 2 is 0.1 so that of event 3 is 0.7. Suppose that the odds ratio for going from A to B for the partial odds of event 1 relative to event 2 is 0.75 and the odds ratio for going from A to B for the partial odds of event 2 relative to event 3 is 2.8 .Determine the probabilities for events 1, 2 and 3 given situation B. Show your work and/or justify your answer.

Explanation / Answer

Let probabilities of event 1,2,3 in B be x,y,z respectively

x/y = 0.2/0.1*0.75 = 1.5

y/z = 2.8*0.1/0.7 = 0.4

or,y=0.4z

or x = 1.5y = 1.5*0.4z = 0.6z

Since,x+y+z = 1

z+0.4z+0.6z = 1

z = 0.5

x=0.6*0.5=0.3

y=0.4*0.5=0.2

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