This is so great, thanks for doing this! The more people internalize this stuff the better—this is “raising the sanity waterline.”
Is there a reason you use superscripts for potential outcomes, and not e.g. Y(a), or Y_a which I see a lot more often?
We define a “Confounder” as anything you need to introduce behind the conditioning sign of the exchangeability
assumption, in order to make the assumption “true”.
A slight technicality is that a “confounder” refers to individual variables, while “confounding” refers to a ternary relation between sets. “Confounding”(A,Y,C) just means adjusting for C gives a valid functional for Y(a), that is conditional ignorability holds: Y(a) independent of A | C. “Confounder”(A,Y,c) (for a singleton c) means ???. It’s not so simple—seemingly reasonable definitions can fail. Tyler wrote a paper with me about this.
Fun exercise: what is the smallest DAG where the definition of a confounder contained in the first sentence on the Wikipedia article on confounding fails.
I think the number of upvotes should count as feedback, and you should put up the entire sequence (if for no other reason than a very handy online reference for future discussions on this topic, and as a way to bridge inference gaps). Causal stuff comes up a fair bit here, and it would be good if we could say “read article X in this sequence to understand what I mean.”
Thank you! I know that you will find a lot of errors in this sequence, so please point them out whenever you see them.
The reason for the superscript is that this was originally written for students in the epidemiology department at HSPH, where superscript is the standard notation due to Prof Hernan’s book. I didn’t want to change all the notation for the Less Wrong adaptation..
I am currently on my phone and will fix the definition of a confounder later tonight when I have access to a real computer. It is probably too early to give a definition before I introduce graphs
Edited to add: The simplest DAG where the definition in the first sentence of Wikipedia fails is when the suspected confounder is a mediator. I think the simplest example where the second definition on Wikipedia fails is M-bias. I will cover M-Bias in Part 3 of the sequence
This is so great, thanks for doing this! The more people internalize this stuff the better—this is “raising the sanity waterline.”
Is there a reason you use superscripts for potential outcomes, and not e.g. Y(a), or Y_a which I see a lot more often?
A slight technicality is that a “confounder” refers to individual variables, while “confounding” refers to a ternary relation between sets. “Confounding”(A,Y,C) just means adjusting for C gives a valid functional for Y(a), that is conditional ignorability holds: Y(a) independent of A | C. “Confounder”(A,Y,c) (for a singleton c) means ???. It’s not so simple—seemingly reasonable definitions can fail. Tyler wrote a paper with me about this.
Fun exercise: what is the smallest DAG where the definition of a confounder contained in the first sentence on the Wikipedia article on confounding fails.
I think the number of upvotes should count as feedback, and you should put up the entire sequence (if for no other reason than a very handy online reference for future discussions on this topic, and as a way to bridge inference gaps). Causal stuff comes up a fair bit here, and it would be good if we could say “read article X in this sequence to understand what I mean.”
edit: may add more later.
Thank you! I know that you will find a lot of errors in this sequence, so please point them out whenever you see them.
The reason for the superscript is that this was originally written for students in the epidemiology department at HSPH, where superscript is the standard notation due to Prof Hernan’s book. I didn’t want to change all the notation for the Less Wrong adaptation..
I am currently on my phone and will fix the definition of a confounder later tonight when I have access to a real computer. It is probably too early to give a definition before I introduce graphs
Edited to add: The simplest DAG where the definition in the first sentence of Wikipedia fails is when the suspected confounder is a mediator. I think the simplest example where the second definition on Wikipedia fails is M-bias. I will cover M-Bias in Part 3 of the sequence
Isn’t the mobile interface just horrifying?