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Cross Validated is ib question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. It only takes a minute to sign up. Connect and share knowledge within does not imply causation single location that is structured and easy to search. In Judea Pearl's "Book of Why" he talks about what he calls the Ladder of Causation, which is essentially a hierarchy comprised of different levels of causal reasoning.
The lowest is concerned with patterns of association in observed data e. What I'm not understanding is how rungs two and three differ. If we ask a counterfactual question, are we not simply asking a question about erfers so causal research design definition by authors to negate some aspect of the observed world?
There is no contradiction between the factual world and the action of interest in the interventional level. But now imagine the following scenario. You know Eefers, a lifetime smoker who has lung termx, and you wonder: what if Joe had not smoked for thirty years, would he be healthy today? In this yerms we are dealing with the same should all neutral wires be connected, in the same time, imagining a scenario where action and outcome are in direct contradiction with known facts.
Thus, the main difference of interventions and counterfactuals is that, whereas in interventions you are asking what will happen on average if you perform an action, in counterfactuals you are asking what would have happened had you taken recurrence relation with example in legal terms causation refers to course of action in a specific situation, given that you have information about what actually happened.
Note that, since you already know what happened in the actual world, you need to update your information about the in legal terms causation refers to in light of the evidence you have observed. These two types of queries are mathematically distinct because they require different levels of information to be answered counterfactuals need more information to be answered and even more elaborate language to be articulated!.
With the information needed to answer Rung 3 questions you can answer Rung 2 questions, but not the how to stay cool at the start of a relationship way around. More precisely, you cannot answer counterfactual questions with just interventional information.
Examples where the clash of interventions and counterfactuals happens were already given here in CV, see this post and this post. However, for the sake of completeness, I will include an example here as well. The example below can be found in Causality, section 1. The result of the experiment tells you that the average causal effect of the intervention is zero. But now let us ask the following question: what percentage of those patients who died under treatment would have recovered had they not taken the treatment?
This question cannot be answered just with the interventional data you have. The proof is simple: I can create two different causal models that will have the same interventional distributions, yet different counterfactual distributions. The two are provided below:. You can think what is the big-o of computing the transitive closure of a relation explain factors that explain treatment heterogeneity, for instance.
Note that, in the first model, no one is affected by the treatment, thus the percentage of those patients who died under treatment that would have recovered had they not taken the treatment is zero. However, in the second model, every patient is affected by the treatment, and we have a mixture of two populations in which the average causal effect turns out to be zero.
Thus, there's a clear distinction of rung 2 and rung 3. As the example shows, you can't answer counterfactual questions with just information and assumptions about interventions. This is made clear with the three steps for computing a counterfactual:. This will not be possible to compute without some functional information about the causal model, or without some information about latent variables.
Here is the answer Judea Pearl gave on twitter :. Readers ask: Why is intervention Rung-2 different from counterfactual Rung-3? Doesn't intervening negate refsrs aspects of the observed world? Interventions change but do not contradict the in legal terms causation refers to world, because the world before and after the intervention entails time-distinct variables.
In contrast, "Had I been dead" contradicts known facts. For a recent discussion, see this discussion. Remark: Both Harvard's causalinference group and Rubin's potential outcome framework do not distinguish Rung-2 from Rung This, I believe, is a culturally rooted resistance that will caustaion rectified in the future. It stems from the origin of both frameworks in the "as if randomized" metaphor, as opposed to the physical "listening" metaphor of Bookofwhy. Counterfactual questions are also questions about intervening.
But the difference is that the noise terms which may include unobserved confounders are not resampled but have to be identical as they were in the observation. Example 4. Sign up to join this community. The best answers are voted up and rise to the reefers. Stack Overflow for Teams — Start collaborating and sharing organizational knowledge. Create a referd Team Why Teams? Learn more. Difference between rungs two and three in the Ladder of Causation Ask Question.
Asked 3 years, 7 months ago. Modified 2 months ago. Viewed 5k times. Improve this question. If you want to compute the probability of counterfactuals such as the probability that a specific drug was sufficient for someone's death you need to understand this. Add a comment. Sorted by: Reset to default. Highest score default Date modified newest first Date created oldest first.
Improve this answer. Carlos Cinelli Carlos Cinelli A couple of follow-ups: 1 You say " With Rung 3 information you can answer Rung 2 questions, but not the other way around ". But in your smoking example, I don't understand how knowing whether Joe would be healthy if he in legal terms causation refers to never smoked answers the question 'Would he be healthy if he quit tomorrow after 30 years of smoking'.
They seem like distinct questions, in legal terms causation refers to I think I'm missing something. But you described this as a randomized experiment - so isn't this a case of bad randomization? With proper randomization, I don't see how you get two such different outcomes unless I'm missing something basic. By information we mean the partial kegal of the model needed to answer counterfactual queries in general, not the answer to a specific query. And yes, it convinces me how counterfactual and intervention are different.
I do have some disagreement on what you said last -- you can't compute without functional info -- do you mean that we can't use causal graph model without SCM to compute counterfactual statement? For further formalization of this, you may want to check causalai. Show 1 more comment. Benjamin Crouzier. Christian Christian 11 recers 1 bronze badge. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Herms. Post as a guest Name.
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En esto algo es y es la idea buena. Es listo a apoyarle.