Thanks again for these clear lectures! Around 2:33 you mention that M is a collider, but I believe it is false. I would go as far as to say the statement is ill-defined because a collider is defined only with respect to a path. So if you look specifically at the path T -> M -> Y, M is not a collider and it doesn't change anything that M is part of an immorality with T and U_M. See Elements of Causal Inference by Peters et al p.82-83. A correct justification for why (most) descendants of T cannot be in the adjustment set is presented in page 113-114 of the same book. I have added "most" in parenthesis because some descendants of T are actually allowed (see Proposition 6.41 (iii)).
Oh, interesting. I get the interpretation that I give in this video from page 339 of Pearl's Causality book. I agree on the definition of a collider as being relative to the path it's on (M is not a collider on the T -> M -> Y path). And I agree that the intervention variable based stuff you point to and what's at the top of page 116 in that book are also nice. It is good for people to check out for a more technical explanation. However, I don't agree that the graphical intuition that I gave is wrong.
@@BradyNealCausalInference I am not sure I understand the argument made at page 339 from Pearl's book so I might be confused. Which unwanted path between T and Y is created by conditioning on Z exactly? Can you write it out? In Pearl it mentions that U_M creates an unblocked backdoor path and writes it out as T U_M -> M -> Y. However I am not sure what T U_M means and I am not sure how it maps to the actual magnified graph.
@@sebastienlachapelle3 I think that argument is generally confusing, which is why I changed it and slightly (to the "new association flowing along T -> M") and hand-waved in this video. I think the backdoor path intuition breaks down in these kinds of examples. For example, there are a lot of graphically unintuitive examples in the Elwert & Winship paper that I link in this lecture. Pearl must have been trying to get the reader to think of a backdoor path like T -> U_M -> M -> Y when he wrote T U_M -> M -> Y, but I think both you and I are weirded out by that. On a related note, now that I'm looking at the ECI book again, it isn't actually completely clear to me where they discuss this issue. It seems like they just state it at the bottom of 115 / top of 116. Would you mind pointing me (and those who are reading because they're interested in learning more about this) more specifically to where they do?
@@BradyNealCausalInference Ok so we agree on the weirdness of Pearl's argument there, cool. At p.113 of ECI, in the paragraph starting with "It is sometimes believed...", there is a sentence starting with "Let us try to investigate...". Starting there and ending at the very end of p.114, they develop sufficient conditions to have a valid adjustment set (defined in Definition 6.38). The actual sufficient condition is given in equation (6.17). This condition is basically exactly the backdoor criterion. Is it what you were asking for?
@@sebastienlachapelle3 The intervention variable argument, right? But then they don't state that you can't condition on descendants of treatment (that aren't ancestors of Y) until the bottom of page 115: "Only the third statement [Shpitser et al., 2010, Perkovic et al., 2015] requires some explanation." The fact that they say it requires explanation means that they don't expect you to understand why the intervention variable argument connects to not conditioning on descendants of treatment. *Fun note:* for anyone reading, the more general version of the backdoor criterion (where you are allowed to condition on descendants of T that aren't ancestors of Y) is called the "adjustment criterion," and it is in that Shpitser et al. (2010) paper.
How do you apply the backdoor adjustment when you have multiple paths from T to Y to get the total causal flow? In your example, you have mediated path via m and a parallel direct path from T to Y. It got me thinking how to apply it when you have N parallel paths. While on the subject, are there methods to collapse parallel paths from T to Y to a single equivalent path?
If you want to get the total causal effect along all causal paths, you just need to not block any of those causal paths. Then, you'll measure the causal flow along all of them in total (after blocking backdoor paths).
define post-treatment and pre-treatment covariates. Pre-treatment covariates seems to be anything allowing association via backdoor paths and post-treatment covariates allows bias on the directed causal path.
Pre-treatment generally means "comes because treatment in time." Importantly, graphically, I mean "is a non-descendant of treatment." Then, for post-treatment, I mean "is a descendant of treatment."
Thanks again for these clear lectures!
Around 2:33 you mention that M is a collider, but I believe it is false. I would go as far as to say the statement is ill-defined because a collider is defined only with respect to a path. So if you look specifically at the path T -> M -> Y, M is not a collider and it doesn't change anything that M is part of an immorality with T and U_M. See Elements of Causal Inference by Peters et al p.82-83.
A correct justification for why (most) descendants of T cannot be in the adjustment set is presented in page 113-114 of the same book. I have added "most" in parenthesis because some descendants of T are actually allowed (see Proposition 6.41 (iii)).
Oh, interesting. I get the interpretation that I give in this video from page 339 of Pearl's Causality book.
I agree on the definition of a collider as being relative to the path it's on (M is not a collider on the T -> M -> Y path). And I agree that the intervention variable based stuff you point to and what's at the top of page 116 in that book are also nice. It is good for people to check out for a more technical explanation. However, I don't agree that the graphical intuition that I gave is wrong.
@@BradyNealCausalInference I am not sure I understand the argument made at page 339 from Pearl's book so I might be confused. Which unwanted path between T and Y is created by conditioning on Z exactly? Can you write it out? In Pearl it mentions that U_M creates an unblocked backdoor path and writes it out as T U_M -> M -> Y. However I am not sure what T U_M means and I am not sure how it maps to the actual magnified graph.
@@sebastienlachapelle3 I think that argument is generally confusing, which is why I changed it and slightly (to the "new association flowing along T -> M") and hand-waved in this video. I think the backdoor path intuition breaks down in these kinds of examples. For example, there are a lot of graphically unintuitive examples in the Elwert & Winship paper that I link in this lecture. Pearl must have been trying to get the reader to think of a backdoor path like T -> U_M -> M -> Y when he wrote T U_M -> M -> Y, but I think both you and I are weirded out by that.
On a related note, now that I'm looking at the ECI book again, it isn't actually completely clear to me where they discuss this issue. It seems like they just state it at the bottom of 115 / top of 116. Would you mind pointing me (and those who are reading because they're interested in learning more about this) more specifically to where they do?
@@BradyNealCausalInference Ok so we agree on the weirdness of Pearl's argument there, cool.
At p.113 of ECI, in the paragraph starting with "It is sometimes believed...", there is a sentence starting with "Let us try to investigate...". Starting there and ending at the very end of p.114, they develop sufficient conditions to have a valid adjustment set (defined in Definition 6.38). The actual sufficient condition is given in equation (6.17). This condition is basically exactly the backdoor criterion.
Is it what you were asking for?
@@sebastienlachapelle3 The intervention variable argument, right? But then they don't state that you can't condition on descendants of treatment (that aren't ancestors of Y) until the bottom of page 115: "Only the third statement [Shpitser et al., 2010, Perkovic et al., 2015] requires
some explanation." The fact that they say it requires explanation means that they don't expect you to understand why the intervention variable argument connects to not conditioning on descendants of treatment.
*Fun note:* for anyone reading, the more general version of the backdoor criterion (where you are allowed to condition on descendants of T that aren't ancestors of Y) is called the "adjustment criterion," and it is in that Shpitser et al. (2010) paper.
4:11 In case of M-bias, what if Z2 is also a confounding variable? Do we have to block both Z2 AND (Z1 and/or Z3)?
How do you apply the backdoor adjustment when you have multiple paths from T to Y to get the total causal flow? In your example, you have mediated path via m and a parallel direct path from T to Y. It got me thinking how to apply it when you have N parallel paths. While on the subject, are there methods to collapse parallel paths from T to Y to a single equivalent path?
If you want to get the total causal effect along all causal paths, you just need to not block any of those causal paths. Then, you'll measure the causal flow along all of them in total (after blocking backdoor paths).
define post-treatment and pre-treatment covariates. Pre-treatment covariates seems to be anything allowing association via backdoor paths and post-treatment covariates allows bias on the directed causal path.
Pre-treatment generally means "comes because treatment in time." Importantly, graphically, I mean "is a non-descendant of treatment." Then, for post-treatment, I mean "is a descendant of treatment."