In the following causal diagram, which of the following are confounding back-door paths for A to F?

For Causal Nodes X,Y:
X and Y will be deconfounded if we block every backdoor, because such paths allow for spurious correlations. 

When eliminating backdoors, we additionally need to ensure that anything closed off from X is not a descendent of X.

Back-Door Criterion

When deconfounding $X$ and $Y$, a back-door path is any path from $X$ to $Y$ that starts with an arrow pointing into $X$. (Notice that if there is a collider on the back-door path, the path is already blocked by the collider.)

The path A <- B <- C -> D -> E is a back-door path for A to E. Forks are also back-door paths.

University of Michigan - Ann Arbor

When the junction $A \leftarrow B \rightarrow C$ appears in a Causal Diagram, we say that B is a confounder for both A and C. It might appear that there is a causal relationship between A and C, because there is an observable relationship between A and C when B is varied. However, if we condition on B ("hold B constant") we observe that A and C become conditionally independent. 

$A \leftarrow B \rightarrow C$: The Fork and Confouders

Pearl, J., & Mackenzie, D. (2018). $\mathit{The \ Book \ of \ Why: \ The \ New \ Science \ of \ Cause \ and \ Effect.}$ Basic Books.

The Book of Why

The classic example of the Confounder effect is the strong association between ice cream sales and crime rate. 

The observed relationship is that as ice cream sales increase, the crime rate increases, however we attribute the increase in ice cream sales and crime rate both to change in season from winter to spring and summer. 

During nice weather, there are more ice cream sales, but also more people outside in close proximity to each other, increasing the potential for crime. 

If we hold the weather constant, we will observe that ice cream sales have no effect on the crime rate.

Example of the Fork and Confounders

Back-door path

A proxy is used as a substitute measure when a variable that is not directly measurable is needed for analysis.  For a variable to be a proxy for another variable, the proxy variable needs to be highly correlated with the variable of interest.  The proxy can be used for any variables such as a mediator, confounder, collider.  

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