Causal Inference in Statistics: Backdoor Criteria Example on p. 62 and 63
I am a reading Judea Pearl's (etc) book Causal Inference in Statistics: A Primer and I'm stuck on an example on p. 62 and 63 that seems very important to understanding the point he's making.
He gives the example of using the backdoor criteria on Figure 2.8 (on p. 48) and points out that to determine an intervention of x on y is trivial because P(y|do(X)) = P(Y|X).
He goes on to ask about what would happen if you adjusted (conditioned) on W. He says this would open a backdoor to influencing Y. But I just can't see how that is the case.
He goes on to explain that W would open the path X -> W <-Z <-> T -> Y. But when I look at Figure 2.8 on 48, I see no double arrow between Z and T. So I don't understand the example or why it opens a backdoor.
causal-diagrams
asked 2 days ago
Bruce Nielson
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I am a reading Judea Pearl's (etc) book Causal Inference in Statistics: A Primer and I'm stuck on an example on p. 62 and 63 that seems very important to understanding the point he's making.
He gives the example of using the backdoor criteria on Figure 2.8 (on p. 48) and points out that to determine an intervention of x on y is trivial because P(y|do(X)) = P(Y|X).
He goes on to ask about what would happen if you adjusted (conditioned) on W. He says this would open a backdoor to influencing Y. But I just can't see how that is the case.
He goes on to explain that W would open the path X -> W <-Z <-> T -> Y. But when I look at Figure 2.8 on 48, I see no double arrow between Z and T. So I don't understand the example or why it opens a backdoor.
causal-diagrams
asked 2 days ago
Bruce Nielson
1
New contributor
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Right after adding this question, I partially answered my own question. I can see now that Figure 2.8 is showing that conditioning on W would open a backdoor to Y because knowing W opens a path to Z which in turn tells you something about T, which in turn tells you something about Y. However, I'm still confused by the way he draws a double arrow between Z and T and what that even means.
– Bruce Nielson
2 days ago
add a comment |
I am a reading Judea Pearl's (etc) book Causal Inference in Statistics: A Primer and I'm stuck on an example on p. 62 and 63 that seems very important to understanding the point he's making.
He gives the example of using the backdoor criteria on Figure 2.8 (on p. 48) and points out that to determine an intervention of x on y is trivial because P(y|do(X)) = P(Y|X).
He goes on to ask about what would happen if you adjusted (conditioned) on W. He says this would open a backdoor to influencing Y. But I just can't see how that is the case.
He goes on to explain that W would open the path X -> W <-Z <-> T -> Y. But when I look at Figure 2.8 on 48, I see no double arrow between Z and T. So I don't understand the example or why it opens a backdoor.
causal-diagrams
asked 2 days ago
Bruce Nielson
1
New contributor
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I am a reading Judea Pearl's (etc) book Causal Inference in Statistics: A Primer and I'm stuck on an example on p. 62 and 63 that seems very important to understanding the point he's making.
He gives the example of using the backdoor criteria on Figure 2.8 (on p. 48) and points out that to determine an intervention of x on y is trivial because P(y|do(X)) = P(Y|X).
He goes on to ask about what would happen if you adjusted (conditioned) on W. He says this would open a backdoor to influencing Y. But I just can't see how that is the case.
He goes on to explain that W would open the path X -> W <-Z <-> T -> Y. But when I look at Figure 2.8 on 48, I see no double arrow between Z and T. So I don't understand the example or why it opens a backdoor.
causal-diagrams
causal-diagrams
asked 2 days ago
Bruce Nielson
1
New contributor
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Bruce Nielson
1
New contributor
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Bruce Nielson
1
New contributor
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 2 days ago
Bruce Nielson
1
asked 2 days ago
Bruce Nielson
1
1
New contributor
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Bruce Nielson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Right after adding this question, I partially answered my own question. I can see now that Figure 2.8 is showing that conditioning on W would open a backdoor to Y because knowing W opens a path to Z which in turn tells you something about T, which in turn tells you something about Y. However, I'm still confused by the way he draws a double arrow between Z and T and what that even means.
– Bruce Nielson
2 days ago
add a comment |
Right after adding this question, I partially answered my own question. I can see now that Figure 2.8 is showing that conditioning on W would open a backdoor to Y because knowing W opens a path to Z which in turn tells you something about T, which in turn tells you something about Y. However, I'm still confused by the way he draws a double arrow between Z and T and what that even means.
– Bruce Nielson
2 days ago
Right after adding this question, I partially answered my own question. I can see now that Figure 2.8 is showing that conditioning on W would open a backdoor to Y because knowing W opens a path to Z which in turn tells you something about T, which in turn tells you something about Y. However, I'm still confused by the way he draws a double arrow between Z and T and what that even means.
– Bruce Nielson
2 days ago
Right after adding this question, I partially answered my own question. I can see now that Figure 2.8 is showing that conditioning on W would open a backdoor to Y because knowing W opens a path to Z which in turn tells you something about T, which in turn tells you something about Y. However, I'm still confused by the way he draws a double arrow between Z and T and what that even means.
– Bruce Nielson
2 days ago
add a comment |
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Bruce Nielson is a new contributor. Be nice, and check out our Code of Conduct.
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Right after adding this question, I partially answered my own question. I can see now that Figure 2.8 is showing that conditioning on W would open a backdoor to Y because knowing W opens a path to Z which in turn tells you something about T, which in turn tells you something about Y. However, I'm still confused by the way he draws a double arrow between Z and T and what that even means.
– Bruce Nielson
2 days ago