  Generalized linear models are often assumed to fit propensity scores, which
are used to compute inverse probability weighted (IPW) estimators. In order to
derive the asymptotic properties of IPW estimators, the propensity score is
supposed to be bounded away from cero. This condition is known in the
literature as strict positivity (or positivity assumption) and, in practice,
when it does not hold, IPW estimators are very unstable and have a large
variability. Although strict positivity is often assumed, it is not upheld when
some of the covariates are continuous. In this work, we attempt to conciliate
between the strict positivity condition and the theory of generalized linear
models by incorporating an extra parameter, which results in an explicit lower
bound for the propensity scores.
