  Causal mediation analysis is complicated with multiple effect definitions
that require different sets of assumptions for identification. This paper
provides a systematic explanation of such assumptions. We define five potential
outcome types whose means are involved in various effect definitions. We tackle
their mean/distribution's identification, starting with the one that requires
the weakest assumptions and gradually building up to the one that requires the
strongest assumptions. This presentation shows clearly why an assumption is
required for one estimand and not another, and provides a succinct table from
which an applied researcher could pick out the assumptions required for
identifying the causal effects they target. Using a running example, the paper
illustrates the assembling and consideration of identifying assumptions for a
range of causal contrasts. For several that are commonly encountered in the
literature, this exercise clarifies that identification requires weaker
assumptions than those often stated in the literature. This attention to the
details also draws attention to the differences in the positivity assumption
for different estimands, with practical implications. Clarity on the
identifying assumptions of these various estimands will help researchers
conduct appropriate mediation analyses and interpret the results with
appropriate caution given the plausibility of the assumptions.
