Propensity scores: Rosenbaum and Rubin (1983) proposed methods of comparing E(y)

for two groups in observational studies while adjusting for possibly confounding variables x. They defined the propensity as the probability of being in one group, as a function of x. They used logistic regression to estimate how propensity depends on x. Their method takes into account differing distributions of the groups on x by using the estimated propensity to match samples from the groups or to subclassify subjects into intervals of propensity scores or to adjust directly by entering the propensity in the model.

Section 5.6: Probit and Complementary Log–Log Models