1Cademy - Front-Door Criterion (Unmeasurable confounder of a mediated path) $\ \ \ \ \ \ \ \ \ \ \ C$ $\ \ \ \ \swarrow \ \ \ \ \ \ \ \ \searrow$ $X \rightarrow M \rightarrow Y$

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Deconfounding/Eliminating Unmeasurable Confounder Variables

Concept

Front-Door Criterion (Unmeasurable confounder of a mediated path)

$\ \ \ \ \ \ \ \ \ \ \ C$

$\ \ \ \ \swarrow \ \ \ \ \ \ \ \ \searrow$

$X \rightarrow M \rightarrow Y$

When the causal effect of a variable $X$ on $Y$ is mediated by a variable $M$ , which is shielded from a confounding set $C$ , if $C$ is unmeasurable, we cannot block the back-door $X \leftarrow C \rightarrow Y$ . So, we use the front-door $X \rightarrow M \rightarrow Y$ .