Back-door path: Difference between revisions

Revision as of 21:19, 2 June 2018

A back-door path in a causal graph is an indirect path with an arrow into the treatment/causal variable.

Formally, given a graph with nodes including $X$ (treatment/causal variable) and $Y$ (outcome variable), a direct path from $X$ to $Y$ is just a directed edge $X\to Y$ . An indirect path from $X$ to $Y$ is some traversal of edges from $X$ to $Y$ that isn't a direct path. Importantly, the edges don't have to be pointed in the "right way", so $X\to Z\leftarrow W\to Y$ is an indirect path. A back-door path is an indirect path with an arrow into $X$ .

"a back-door path is defined as any path between the causal variable and the outcome variable that begins with an arrow that points to the causal variable" (p. 30).^[1]

Examples

$X\leftarrow Z\to Y$ is a back-door path from $X$ to $Y$ .

$X\to Z\leftarrow W\to Y$ is not a back-door path from $X$ to $Y$ : it is an indirect path but there is no arrow into $X$ .

↑ Stephen L. Morgan; Christopher Winship. Counterfactual and Causal Inference: Methods and Principles for Social Research. 2nd ed. Cambridge University Press. 2015.

[1] Stephen L. Morgan; Christopher Winship. Counterfactual and Causal Inference: Methods and Principles for Social Research. 2nd ed. Cambridge University Press. 2015.

[1]

@@ Line 1: / Line 1: @@
-A '''back-door path''' in a [[causal graph]] is an indirect path with an arrow into the treatment variable.
+A '''back-door path''' in a [[causal graph]] is an indirect path with an arrow into the treatment/causal variable.
-Formally, given a graph with nodes including <math>X</math> (treatment variable) and <math>Y</math> (outcome variable), a direct path from <math>X</math> to <math>Y</math> is just a directed edge <math>X \to Y</math>. An indirect path from <math>X</math> to <math>Y</math> is some traversal of edges from <math>X</math> to <math>Y</math> that isn't a direct path. Importantly, the edges don't have to be pointed in the "right way", so <math>X \to Z \leftarrow W \to Y</math> is an indirect path. A back-door path is an indirect path with an arrow into <math>X</math>.
+Formally, given a graph with nodes including <math>X</math> (treatment/causal variable) and <math>Y</math> (outcome variable), a direct path from <math>X</math> to <math>Y</math> is just a directed edge <math>X \to Y</math>. An indirect path from <math>X</math> to <math>Y</math> is some traversal of edges from <math>X</math> to <math>Y</math> that isn't a direct path. Importantly, the edges don't have to be pointed in the "right way", so <math>X \to Z \leftarrow W \to Y</math> is an indirect path. A back-door path is an indirect path with an arrow into <math>X</math>.
+"a back-door path is defined as any path between the causal variable and the outcome variable that begins with an arrow that points to the causal variable" (p. 30).<ref>Stephen L. Morgan; Christopher Winship. ''Counterfactual and Causal Inference: Methods and Principles for Social Research''. 2nd ed. Cambridge University Press. 2015.</ref>
 ==Examples==