Question

2.13 Starting from the unconditional product-binomial likelihood (2.53) we now use a logit (logistic) model to derive the conditional hypergeometric distribution for a 2x2 table. Conditional on ni and nz (or ni, N), under the logistic model we can express the logit of Ti and 712 as los ( ---) = a +B105 ( 1 --) = a. (2.181) 2.13.1. Show that the inverse logits are provided by logistic functions of the form eatß T1 = T2 = (2.182) 1 teatß' 1 tea

Answer 1

biven, briver log ( 2 1 1 1 = 28 Now loge ( 7 ) = 448 B = d. - B - x, ex413 9,47,624B - eat B R. (1+ B) B 1 9 = ex+ B ltedt 13 And & 2 ze ze 1-72 722 &- (1-22) 22 = 8x - 72 ek. *2(lterl=et tea