I still don’t understand why the equation doesn’t hold. I mean, it terms of mathematics, there’s nothing prevent it to be true ... you just write out explicitly what Y(1) and Y(0) are
I guess I figure it out. E[Y|T=1] means the expected outcome in the group of people who get treatment. So E[Y|T=1] - E[Y|T=0] is an associational quantity. The explicitly of Y(1) should be E[Y|do(T=1)]
Hey! Can someone please help me understand if it is only the disproportional quantities of some biasing features that are making the groups non comparable? In other words: If I force both of my groups (sleeping with and without shoes on) to have the same proportion of drunk people, will I have my groups comparable?
Hello Brady. So, you say that if there are more than one covariate then the treatment groups should be comparable across all of them for average treatment effect to be equal to associational difference. So, my question is, do all these covariates have to be common causes of both treatment variable and outcome variable?
about regression coefficient, I have some questions. Since correlation is not causation, is the coefficient of linear regression Y on X not the causal effect of X on Y? At this time, what this coefficent is used for? Just can be used for prediction or not? Then when can the coefficient of regression be used for causal explanation, maybe when all the confounders between X and Y are included as regressors? or are there some other situations? And i remeber people always regression to do causal inference. so, in a word, I'm so confused about the explanation of regression coefficients. About this, are there some literature?
"Since correlation is not causation, is the coefficient of linear regression Y on X not the causal effect of X on Y?" That's right. "At this time, what this coefficent is used for? Just can be used for prediction or not?" Right, just prediction. "Then when can the coefficient of regression be used for causal explanation, maybe when all the confounders between X and Y are included as regressors?" Right, assuming that the linear model is well-specified (that the outcome is generated by a linear function of the confounders and X). My favorite discussion of the cons of regression coefficients for causal effect estimation is in the Morgan & Winship book that I think I reference at the end of the lecture.
@@BradyNealCausalInference Appreciate it Brady! Really learned a lot from your video. I guess one issue with adding tons of covariates in the linear model is that we will lose a lot of power since there are more parameters to estimate. In a more extreme case, we will have more variables than sample size.
i don't really understand ''there could be other covariates that are important to be comparable across''. Does it mean that although the 2 groups are comparable along the covariate which is whether they go to sleep drunk or not, if there is one other covariate that makes them uncomparable, we still don't have this equality? about this may I ask a more specific explanation or a example? looking forward to your reply and thank you very much！
That's right! Basically, there could be other covariates that you need to condition on to get exchangeability (discussed in another lecture this week). And then, we'll see a graphical perspective on this in weeks 3 and 4. For now, you can think of it as important to condition on any common causes of T and Y.
@@BradyNealCausalInference I also have another question. I'm wondering if 'confounding' or 'confounder' has specific definitions and are there any methods or rules to help us identify the confounding or confounders?
@@shirobin371 I thinking of "confounding" as unblocked backdoor paths (we see these in week 3), and I think this is a common graphical definition. For "confounders," check out "On the definition of a confounder" here: www.ncbi.nlm.nih.gov/pmc/articles/PMC4276366/
You can think of two groups being comparable if they have the same distribution of covariates. Check out this part of this future lecture where I define covariate balance: th-cam.com/video/kgbRoHfb6SI/w-d-xo.htmlm10s
The questions at the end are a great addition!
And honestly not that easy! Great content.
Wow. Amazing work. What a blessing it is to have access to this videos with such amazing explanations. Thank you so much.
I sincerely thank your lecture and great explanations. from Korea
The groups are not comparable because the data is not IID. Awesome video!
You covered perfectly the first session. Now understand better
laugh hard at this 5:11 why is this sober guy going to sleep with his shoes on? By the way, thanks for the lecture!
Awesome, now I understand!
If Y|do(T=1) is approximated as Y(1). E[Y(1)] = E[Y|T=1] is just notationally same right. Then why it isn't the same?
I still don’t understand why the equation doesn’t hold. I mean, it terms of mathematics, there’s nothing prevent it to be true ... you just write out explicitly what Y(1) and Y(0) are
I guess I figure it out. E[Y|T=1] means the expected outcome in the group of people who get treatment. So E[Y|T=1] - E[Y|T=0] is an associational quantity. The explicitly of Y(1) should be E[Y|do(T=1)]
Hey!
Can someone please help me understand if it is only the disproportional quantities of some biasing features that are making the groups non comparable?
In other words:
If I force both of my groups (sleeping with and without shoes on) to have the same proportion of drunk people, will I have my groups comparable?
Hello Brady. So, you say that if there are more than one covariate then the treatment groups should be comparable across all of them for average treatment effect to be equal to associational difference. So, my question is, do all these covariates have to be common causes of both treatment variable and outcome variable?
I lost it at the reddit post 😭😭😭😭
about regression coefficient, I have some questions. Since correlation is not causation, is the coefficient of linear regression Y on X not the causal effect of X on Y? At this time, what this coefficent is used for? Just can be used for prediction or not? Then when can the coefficient of regression be used for causal explanation, maybe when all the confounders between X and Y are included as regressors? or are there some other situations? And i remeber people always regression to do causal inference. so, in a word, I'm so confused about the explanation of regression coefficients. About this, are there some literature?
"Since correlation is not causation, is the coefficient of linear regression Y on X not the causal effect of X on Y?"
That's right.
"At this time, what this coefficent is used for? Just can be used for prediction or not?"
Right, just prediction.
"Then when can the coefficient of regression be used for causal explanation, maybe when all the confounders between X and Y are included as regressors?"
Right, assuming that the linear model is well-specified (that the outcome is generated by a linear function of the confounders and X).
My favorite discussion of the cons of regression coefficients for causal effect estimation is in the Morgan & Winship book that I think I reference at the end of the lecture.
@@BradyNealCausalInference come to think of it, yes, you did reference and I'll read it later. Thanks a lot!
@@BradyNealCausalInference Appreciate it Brady! Really learned a lot from your video.
I guess one issue with adding tons of covariates in the linear model is that we will lose a lot of power since there are more parameters to estimate. In a more extreme case, we will have more variables than sample size.
i don't really understand ''there could be other covariates that are important to be comparable across''. Does it mean that although the 2 groups are comparable along the covariate which is whether they go to sleep drunk or not, if there is one other covariate that makes them uncomparable, we still don't have this equality? about this may I ask a more specific explanation or a example? looking forward to your reply and thank you very much！
That's right! Basically, there could be other covariates that you need to condition on to get exchangeability (discussed in another lecture this week). And then, we'll see a graphical perspective on this in weeks 3 and 4. For now, you can think of it as important to condition on any common causes of T and Y.
@@BradyNealCausalInference Thank you，I get it
@@BradyNealCausalInference I also have another question. I'm wondering if 'confounding' or 'confounder' has specific definitions and are there any methods or rules to help us identify the confounding or confounders?
@@shirobin371 I thinking of "confounding" as unblocked backdoor paths (we see these in week 3), and I think this is a common graphical definition. For "confounders," check out "On the definition of a confounder" here: www.ncbi.nlm.nih.gov/pmc/articles/PMC4276366/
@@BradyNealCausalInference I will read it. Thanks a lot!
May I ask how to quantify the comparability of two treatment groups?
You can think of two groups being comparable if they have the same distribution of covariates.
Check out this part of this future lecture where I define covariate balance:
th-cam.com/video/kgbRoHfb6SI/w-d-xo.htmlm10s