Authors: Drago Plecko
Abstract: Relationships of cause and effect are of prime importance for explaining
scientific phenomena. Often, rather than just understanding the effects of
causes, researchers also wish to understand how a cause $X$ affects an outcome
$Y$ mechanistically — i.e., what are the causal pathways that are activated
between $X$ and $Y$. For analyzing such questions, a range of methods has been
developed over decades under the rubric of causal mediation analysis.
Traditional mediation analysis focuses on decomposing the average treatment
effect (ATE) into direct and indirect effects, and therefore focuses on the ATE
as the central quantity. This corresponds to providing explanations for
associations in the interventional regime, such as when the treatment $X$ is
randomized. Commonly, however, it is of interest to explain associations in the
observational regime, and not just in the interventional regime. In this paper,
we introduce \text{variation analysis}, an extension of mediation analysis that
focuses on the total variation (TV) measure between $X$ and $Y$, written as
$\mathrm{E}[Y \mid X=x_1] – \mathrm{E}[Y \mid X=x_0]$. The TV measure
encompasses both causal and confounded effects, as opposed to the ATE which
only encompasses causal (direct and mediated) variations. In this way, the TV
measure is suitable for providing explanations in the natural regime and
answering questions such as “why is $X$ associated with $Y$?”. Our focus is
on decomposing the TV measure, in a way that explicitly includes direct,
indirect, and confounded variations. Furthermore, we also decompose the TV
measure to include interaction terms between these different pathways.
Subsequently, interaction testing is introduced, involving hypothesis tests to
determine if interaction terms are significantly different from zero. If
interactions are not significant, more parsimonious decompositions of the TV
measure can be used.
Source: http://arxiv.org/abs/2411.08861v1
