causal inference
1. do operator
- to clear up some early confusions I had
- the do operator is what we would like to do in the ideal world where we have control over everything
- but we don't live in that world, so often we approximate this operation using a formula over observational data
2. graphical models
- arrows indicate a causal relationship
- mediators
- common effects
- ancestors are conditionally dependent on common effects
- common causes
- descendents are conditionally independent on common causes
3. backdoor path
- a path is blocked if (a) we control for a non-collider on the path (control for a common cause) or we (b) don't control for a collider
- if all backdoor paths between \(X\) and \(Y\) are blocked by \(Z\), then the causal effect of \(X\) on \(Y\) can be determined by marginalizing out \(Z\) (see controlling confounding bias).
- What happens if all backdoor paths are not blocked? Then there will be a non-causal relationship between \(X\) and \(Y\) that will be mis-interpreted as a causal effect, i.e. \(X\) and \(Y\) will be dependent, but not because of anything causal.
4. what do the arrows mean?
- the arrows show where casual effects flow?
- here for what scientists believe about their models
5. what does blocking mean?
- There can exist causal relationships between variables.
- There can also exist non-causal associations between variables (see common-cause in confounds)
- A path is blocked if a non-collider along the path is conditioned on or if there is a collider that is not conditioned on
- see also here for what blocking means and here for colliders