  This paper aims to provide practitioners of causal mediation analysis with a
better understanding of estimation options. We take as inputs two familiar
strategies (weighting and model-based prediction) and a simple way of combining
them (weighted models), and show how a range of estimators can be generated,
with different modeling requirements and robustness properties. The primary
goal is to help build intuitive appreciation for robust estimation that is
conducive to sound practice. A second goal is to provide a "menu" of estimators
that practitioners can choose from for the estimation of marginal natural
(in)direct effects. The estimators generated from this exercise include some
that coincide or are similar to existing estimators and others that have not
previously appeared in the literature. We note several different ways to
estimate the weights for cross-world weighting based on three expressions of
the weighting function, including one that is novel; and show how to check the
resulting covariate and mediator balance. We use a random continuous weights
bootstrap to obtain confidence intervals, and also derive general asymptotic
variance formulas for the estimators. The estimators are illustrated using data
from an adolescent alcohol use prevention study.
