The logit and probit links are symmetric, because the probabilities
approach zero or one at the same rate. The log-log and complementary
log-log links are asymmetric. Complementary log-log links approach
zero slowly and one quickly. Log-log links approach zero quickly and
one slowly. Either the log-log or complementary log-log link will tend
to fit better than logistic and probit, and are frequently used when
the probability of an event is small or large. A mixture of the two
links, the log-log and complementary log-log is often used, where each
link is weighted. The reason that logit is so prevalent is because
logistic parameters can be interpreted as odds ratios.