In interpreting the binary regression models often used in the analysi
s of dose-response data, it is common to introduce the idea of an unde
rlying continuous tolerance distribution. Different choices of link fu
nction lead to different tolerance distributions. A useful way of comp
aring these alternatives is to compare the hazard functions or tail fu
nctions associated with each tolerance distribution. Tail functions ca
n also be applied to give numerically preferable formulas for the iter
ative weights and the adjusted dependent variable in the fitting of bi
nary regression models by the iteratively reweighted least-squares alg
orithm.