Rsc115: Sampling Bias and Logistic Models

Biased sampling It is worth re-stating the point made in section 3.3, using Meng’s notation in which Oi = 1 indicates that unit i will volunteer if asked. We distinguish between the conditional distribution pn(x,y |o ≡ 1) given that a fixed sample of n individuals happens to have no refusers, and the distribution po=1(x,y) for the first n volunteers. In a random-effects model where the responses for distinct units are correlated, these distributions are usually different. Longford will be disappointed to learn that the conditional distributions pn(y |x,o ≡ 1) and po=1(y |x) are seldom equal either. Whether they are the same or different, it is the stratum distribution po=1(x,y) that is relevant for volunteer samples.