10
个编辑
更改
跳到导航
跳到搜索
第1行：
第1行： + + + + + + + + 第10行：
第18行： + + + + + + 第20行：
第34行： + + + + 第30行：
第48行： + + + + + + 第50行：
第74行： + + + + 第56行：
第84行： + + + + + + + + 第64行：
第100行： + + + + + + + + + + 第77行：
第123行： + + + + 第101行：
第151行： + + + + 第107行：
第161行： + + + + 第115行：
第173行： + + + + 第135行：
第197行： + + + + + + + 第159行：
第228行： + + + + + + + + 第185行：
第262行： + + 第206行：
第285行： + + 第227行：
第308行： + + + + 第251行：
第336行： + + + + + + 第277行：
第368行： + + 第298行：
第391行： + + + + + + + +
无编辑摘要
The Rubin causal model (RCM), also known as the Neyman–Rubin causal model,[1] is an approach to the statistical analysis of cause and effect based on the framework of potential outcomes, named after Donald Rubin. The name "Rubin causal model" was first coined by Paul W. Holland.[2] The potential outcomes framework was first proposed by Jerzy Neyman in his 1923 Master's thesis,[3] though he discussed it only in the context of completely randomized experiments.[4] Rubin extended it into a general framework for thinking about causation in both observational and experimental studies.[1]
鲁宾因果模型 (RCM)，也称为 Neyman-Rubin 因果模型，<ref name="sekhon">{{cite book |last=Sekhon |first=Jasjeet |chapter=The Neyman–Rubin Model of Causal Inference and Estimation via Matching Methods |title=The Oxford Handbook of Political Methodology |year=2007 |chapter-url=http://sekhon.berkeley.edu/papers/SekhonOxfordHandbook.pdf }}</ref>是一种基于潜在结果框架的因果统计分析方法，以Donald Rubin的名字命名。“鲁宾因果模型”这个名字最早是由 Paul W. Holland 创造的。 <ref name="holland:causal86">{{cite journal |last=Holland |first=Paul W. |title=Statistics and Causal Inference |journal=[[Journal of the American Statistical Association|J. Amer. Statist. Assoc.]] |volume=81 |issue=396 |year=1986 |pages=945–960 |jstor=2289064 |doi=10.1080/01621459.1986.10478354}}</ref>潜在结果框架最初是由 Jerzy Neyman 在他 1923 年的硕士论文中提出的，<ref name="neyman:masters">Neyman, Jerzy. ''Sur les applications de la theorie des probabilites aux experiences agricoles: Essai des principes.'' Master's Thesis (1923). Excerpts reprinted in English, Statistical Science, Vol. 5, pp. 463–472. ([[Dorota Dabrowska|D. M. Dabrowska]], and T. P. Speed, Translators.)</ref>尽管他只在完全随机实验的背景下讨论了它。 <ref name="Jasa1">{{cite journal |last=Rubin |first=Donald |year=2005 |title=Causal Inference Using Potential Outcomes |journal=[[Journal of the American Statistical Association|J. Amer. Statist. Assoc.]] |volume=100 |issue=469 |pages=322–331 |doi=10.1198/016214504000001880 }}</ref>鲁宾将其扩展为在观察性和实验性研究中思考因果关系的一般框架。<ref name="sekhon"/>
鲁宾因果模型 (RCM)，也称为 Neyman-Rubin 因果模型，<ref name="sekhon">{{cite book |last=Sekhon |first=Jasjeet |chapter=The Neyman–Rubin Model of Causal Inference and Estimation via Matching Methods |title=The Oxford Handbook of Political Methodology |year=2007 |chapter-url=http://sekhon.berkeley.edu/papers/SekhonOxfordHandbook.pdf }}</ref>是一种基于潜在结果框架的因果统计分析方法，以Donald Rubin的名字命名。“鲁宾因果模型”这个名字最早是由 Paul W. Holland 创造的。 <ref name="holland:causal86">{{cite journal |last=Holland |first=Paul W. |title=Statistics and Causal Inference |journal=[[Journal of the American Statistical Association|J. Amer. Statist. Assoc.]] |volume=81 |issue=396 |year=1986 |pages=945–960 |jstor=2289064 |doi=10.1080/01621459.1986.10478354}}</ref>潜在结果框架最初是由 Jerzy Neyman 在他 1923 年的硕士论文中提出的，<ref name="neyman:masters">Neyman, Jerzy. ''Sur les applications de la theorie des probabilites aux experiences agricoles: Essai des principes.'' Master's Thesis (1923). Excerpts reprinted in English, Statistical Science, Vol. 5, pp. 463–472. ([[Dorota Dabrowska|D. M. Dabrowska]], and T. P. Speed, Translators.)</ref>尽管他只在完全随机实验的背景下讨论了它。 <ref name="Jasa1">{{cite journal |last=Rubin |first=Donald |year=2005 |title=Causal Inference Using Potential Outcomes |journal=[[Journal of the American Statistical Association|J. Amer. Statist. Assoc.]] |volume=100 |issue=469 |pages=322–331 |doi=10.1198/016214504000001880 }}</ref>鲁宾将其扩展为在观察性和实验性研究中思考因果关系的一般框架。<ref name="sekhon"/>
==介绍==
==介绍==
The Rubin causal model is based on the idea of potential outcomes. For example, a person would have a particular income at age 40 if he had attended college, whereas he would have a different income at age 40 if he had not attended college. To measure the causal effect of going to college for this person, we need to compare the outcome for the same individual in both alternative futures. Since it is impossible to see both potential outcomes at once, one of the potential outcomes is always missing. This dilemma is the "fundamental problem of causal inference".
Because of the fundamental problem of causal inference, unit-level causal effects cannot be directly observed. However, randomized experiments allow for the estimation of population-level causal effects.[5] A randomized experiment assigns people randomly to treatments: college or no college. Because of this random assignment, the groups are (on average) equivalent, and the difference in income at age 40 can be attributed to the college assignment since that was the only difference between the groups. An estimate of the average causal effect (also referred to as the average treatment effect) can then be obtained by computing the difference in means between the treated (college-attending) and control (not-college-attending) samples.
In many circumstances, however, randomized experiments are not possible due to ethical or practical concerns. In such scenarios there is a non-random assignment mechanism. This is the case for the example of college attendance: people are not randomly assigned to attend college. Rather, people may choose to attend college based on their financial situation, parents' education, and so on. Many statistical methods have been developed for causal inference, such as propensity score matching. These methods attempt to correct for the assignment mechanism by finding control units similar to treatment units.
鲁宾因果模型基于潜在结果的想法。例如，如果一个人上过大学，他在 40 岁时会有特定的收入，而如果他没有上过大学，他在 40 岁时会有不同的收入。为了衡量这个人上大学的因果效应，我们需要比较同一个人在两种不同的未来中的结果。由于不可能同时看到两种潜在结果，因此总是缺少其中一种潜在结果。这种困境就是“因果推理的基本问题”。
鲁宾因果模型基于潜在结果的想法。例如，如果一个人上过大学，他在 40 岁时会有特定的收入，而如果他没有上过大学，他在 40 岁时会有不同的收入。为了衡量这个人上大学的因果效应，我们需要比较同一个人在两种不同的未来中的结果。由于不可能同时看到两种潜在结果，因此总是缺少其中一种潜在结果。这种困境就是“因果推理的基本问题”。
==一个扩展案例==
==一个扩展案例==
Rubin defines a causal effect:
Intuitively, the causal effect of one treatment, E, over another, C, for a particular unit and an interval of time from {\displaystyle t_{1}}t_{1} to {\displaystyle t_{2}}t_{2} is the difference between what would have happened at time {\displaystyle t_{2}}t_{2} if the unit had been exposed to E initiated at {\displaystyle t_{1}}t_{1} and what would have happened at {\displaystyle t_{2}}t_{2} if the unit had been exposed to C initiated at {\displaystyle t_{1}}t_{1}: 'If an hour ago I had taken two aspirins instead of just a glass of water, my headache would now be gone,' or 'because an hour ago I took two aspirins instead of just a glass of water, my headache is now gone.' Our definition of the causal effect of the E versus C treatment will reflect this intuitive meaning."[5]
According to the RCM, the causal effect of your taking or not taking aspirin one hour ago is the difference between how your head would have felt in case 1 (taking the aspirin) and case 2 (not taking the aspirin). If your headache would remain without aspirin but disappear if you took aspirin, then the causal effect of taking aspirin is headache relief. In most circumstances, we are interested in comparing two futures, one generally termed "treatment" and the other "control". These labels are somewhat arbitrary.
鲁宾定义了一个因果效应：
鲁宾定义了一个因果效应：
===潜在结果===
===潜在结果===
Potential outcomes
Suppose that Joe is participating in an FDA test for a new hypertension drug. If we were omniscient, we would know the outcomes for Joe under both treatment (the new drug) and control (either no treatment or the current standard treatment). The causal effect, or treatment effect, is the difference between these two potential outcomes.
假设 Joe 正在参加 FDA 对一种新的高血压药物的测试。如果我们无所不知，我们就会知道乔在处理（新药）和控制（未处理或当前标准处理）下的结果。因果效应或处理效应是这两种潜在结果之间的差异。
假设 Joe 正在参加 FDA 对一种新的高血压药物的测试。如果我们无所不知，我们就会知道乔在处理（新药）和控制（未处理或当前标准处理）下的结果。因果效应或处理效应是这两种潜在结果之间的差异。
|}
|}
Y_{t}(u) is Joe's blood pressure if he takes the new pill. In general, this notation expresses the potential outcome which results from a treatment, t, on a unit, u. Similarly, {\displaystyle Y_{c}(u)}Y_{c}(u) is the effect of a different treatment, c or control, on a unit, u. In this case, {\displaystyle Y_{c}(u)}Y_{c}(u) is Joe's blood pressure if he doesn't take the pill. {\displaystyle Y_{t}(u)-Y_{c}(u)}Y_{t}(u)-Y_{c}(u) is the causal effect of taking the new drug.
From this table we only know the causal effect on Joe. Everyone else in the study might have an increase in blood pressure if they take the pill. However, regardless of what the causal effect is for the other subjects, the causal effect for Joe is lower blood pressure, relative to what his blood pressure would have been if he had not taken the pill.
Consider a larger sample of patients:
如果乔服用新药丸，<math>Y_{t}(u)</math>就是他的血压。通常，该符号表示对单位u进行处理t 所产生的潜在结果。类似的，<math>Y_{c}(u)</math>是不同处理t或控制c对单元u的影响。在这种情况下，如果乔不服药，<math>Y_{c}(u)</math>就是他的血压。<math>Y_{t}(u)-Y_{c}(u)</math> 是服用新药的因果效应。
如果乔服用新药丸，<math>Y_{t}(u)</math>就是他的血压。通常，该符号表示对单位u进行处理t 所产生的潜在结果。类似的，<math>Y_{c}(u)</math>是不同处理t或控制c对单元u的影响。在这种情况下，如果乔不服药，<math>Y_{c}(u)</math>就是他的血压。<math>Y_{t}(u)-Y_{c}(u)</math> 是服用新药的因果效应。
|}
|}
The causal effect is different for every subject, but the drug works for Joe, Mary and Bob because the causal effect is negative. Their blood pressure is lower with the drug than it would have been if each did not take the drug. For Sally, on the other hand, the drug causes an increase in blood pressure.
In order for a potential outcome to make sense, it must be possible, at least a priori. For example, if there is no way for Joe, under any circumstance, to obtain the new drug, then {\displaystyle Y_{t}(u)}Y_{t}(u) is impossible for him. It can never happen. And if {\displaystyle Y_{t}(u)}Y_{t}(u) can never be observed, even in theory, then the causal effect of treatment on Joe's blood pressure is not defined.
因果效应对于每一个主题是不同的，但药物对乔，玛丽和鲍勃都有影响，因为因果效应是负的。他们服用药物后的血压低于每个人不服用药物时的血压。另一方面，对于 Sally 来说，这种药物会导致血压升高。
因果效应对于每一个主题是不同的，但药物对乔，玛丽和鲍勃都有影响，因为因果效应是负的。他们服用药物后的血压低于每个人不服用药物时的血压。另一方面，对于 Sally 来说，这种药物会导致血压升高。
===没有操纵就没有因果关系===
===没有操纵就没有因果关系===
No causation without manipulation
The causal effect of new drug is well defined because it is the simple difference of two potential outcomes, both of which might happen. In this case, we (or something else) can manipulate the world, at least conceptually, so that it is possible that one thing or a different thing might happen.
This definition of causal effects becomes much more problematic if there is no way for one of the potential outcomes to happen, ever. For example, what is the causal effect of Joe's height on his weight? Naively, this seems similar to our other examples. We just need to compare two potential outcomes: what would Joe's weight be under the treatment (where treatment is defined as being 3 inches taller) and what would Joe's weight be under the control (where control is defined as his current height).
A moment's reflection highlights the problem: we can't increase Joe's height. There is no way to observe, even conceptually, what Joe's weight would be if he were taller because there is no way to make him taller. We can't manipulate Joe's height, so it makes no sense to investigate the causal effect of height on weight. Hence the slogan: No causation without manipulation.
新药的因果效应是明确定义的，因为它是两种可能发生的潜在结果的简单差异。在这种情况下，我们（或其他事物）可以干预世界，至少在概念上是这样，因此可能会发生不同的事。
新药的因果效应是明确定义的，因为它是两种可能发生的潜在结果的简单差异。在这种情况下，我们（或其他事物）可以干预世界，至少在概念上是这样，因此可能会发生不同的事。
===稳定单元处理值假设 (SUTVA)===
===稳定单元处理值假设 (SUTVA)===
Stable unit treatment value assumption (SUTVA)
See also: Spillover (experiment)
We require that "the [potential outcome] observation on one unit should be unaffected by the particular assignment of treatments to the other units" (Cox 1958, §2.4). This is called the stable unit treatment value assumption (SUTVA), which goes beyond the concept of independence.
In the context of our example, Joe's blood pressure should not depend on whether or not Mary receives the drug. But what if it does? Suppose that Joe and Mary live in the same house and Mary always cooks. The drug causes Mary to crave salty foods, so if she takes the drug she will cook with more salt than she would have otherwise. A high salt diet increases Joe's blood pressure. Therefore, his outcome will depend on both which treatment he received and which treatment Mary receives.
SUTVA violation makes causal inference more difficult. We can account for dependent observations by considering more treatments. We create 4 treatments by taking into account whether or not Mary receives treatment.
我们要求“对一个单元的 [潜在结果] 观察不应受到其他单元的特定处理分配的影响”（Cox 1958，第 2.4 节）。这被称为稳定单元处理值假设（SUTVA），它超越了独立性的概念。
我们要求“对一个单元的 [潜在结果] 观察不应受到其他单元的特定处理分配的影响”（Cox 1958，第 2.4 节）。这被称为稳定单元处理值假设（SUTVA），它超越了独立性的概念。
!乔||140||130||125||120
!乔||140||130||125||120
|}
|}
Recall that a causal effect is defined as the difference between two potential outcomes. In this case, there are multiple causal effects because there are more than two potential outcomes. One is the causal effect of the drug on Joe when Mary receives treatment and is calculated, {\displaystyle 130-140}{\displaystyle 130-140}. Another is the causal effect on Joe when Mary does not receive treatment and is calculated {\displaystyle 120-125}{\displaystyle 120-125}. The third is the causal effect of Mary's treatment on Joe when Joe is not treated. This is calculated as {\displaystyle 140-125}{\displaystyle 140-125}. The treatment Mary receives has a greater causal effect on Joe than the treatment which Joe received has on Joe, and it is in the opposite direction.
By considering more potential outcomes in this way, we can cause SUTVA to hold. However, if any units other than Joe are dependent on Mary, then we must consider further potential outcomes. The greater the number of dependent units, the more potential outcomes we must consider and the more complex the calculations become (consider an experiment with 20 different people, each of whom's treatment status can effect outcomes for every one else). In order to (easily) estimate the causal effect of a single treatment relative to a control, SUTVA should hold.
回想一下，因果效应被定义为两个潜在结果之间的差异。在这种情况下，存在多种因果效应，因为存在两个以上的潜在结果。一是玛丽接受处理时药物对乔的因果效应<math>130-140</math>。另一个是当玛丽没有接受处理时对乔的因果效应<math>120-125</math>。第三是在乔没有得到处理的情况下，玛丽的处理对乔的因果效应<math>140-125</math>。Mary 接受的处理对 Joe 的因果影响比 Joe 接受的处理对 Joe 的影响更大，而且是相反的方向。
回想一下，因果效应被定义为两个潜在结果之间的差异。在这种情况下，存在多种因果效应，因为存在两个以上的潜在结果。一是玛丽接受处理时药物对乔的因果效应<math>130-140</math>。另一个是当玛丽没有接受处理时对乔的因果效应<math>120-125</math>。第三是在乔没有得到处理的情况下，玛丽的处理对乔的因果效应<math>140-125</math>。Mary 接受的处理对 Joe 的因果影响比 Joe 接受的处理对 Joe 的影响更大，而且是相反的方向。
!吝啬的||135||143||−8
!吝啬的||135||143||−8
|}
|}
One may calculate the average causal effect by taking the mean of all the causal effects.
How we measure the response affects what inferences we draw. Suppose that we measure changes in blood pressure as a percentage change rather than in absolute values. Then, depending in the exact numbers, the average causal effect might be an increase in blood pressure. For example, assume that George's blood pressure would be 154 under control and 140 with treatment. The absolute size of the causal effect is −14, but the percentage difference (in terms of the treatment level of 140) is −10%. If Sarah's blood pressure is 200 under treatment and 184 under control, then the causal effect in 16 in absolute terms but 8% in terms of the treatment value. A smaller absolute change in blood pressure (−14 versus 16) yields a larger percentage change (−10% versus 8%) for George. Even though the average causal effect for George and Sarah is +1 in absolute terms, it is −1 in percentage terms.
人们可以通过取所有因果效应的平均值来计算平均因果效应。
人们可以通过取所有因果效应的平均值来计算平均因果效应。
===因果推理的基本问题===
===因果推理的基本问题===
The fundamental problem of causal inference
The results we have seen up to this point would never be measured in practice. It is impossible, by definition, to observe the effect of more than one treatment on a subject over a specific time period. Joe cannot both take the pill and not take the pill at the same time. Therefore, the data would look something like this:
到目前为止，我们所看到的结果永远无法在实践中衡量。根据定义，不可能在特定时间段内观察多种处理对受试者的影响。乔不能同时服用避孕药和不服用避孕药。因此，数据看起来像这样：
到目前为止，我们所看到的结果永远无法在实践中衡量。根据定义，不可能在特定时间段内观察多种处理对受试者的影响。乔不能同时服用避孕药和不服用避孕药。因此，数据看起来像这样：
!乔||130||?||?
!乔||130||?||?
|}
|}
Question marks are responses that could not be observed. The Fundamental Problem of Causal Inference[2] is that directly observing causal effects is impossible. However, this does not make causal inference impossible. Certain techniques and assumptions allow the fundamental problem to be overcome.
Assume that we have the following data:
问号是无法观察到的反馈。因果推断的基本问题<ref name="holland:causal86"/>是不可能直接观察因果效应。然而，这并不使因果推断成为不可能。某些技术和假设可以克服基本问题。
问号是无法观察到的反馈。因果推断的基本问题<ref name="holland:causal86"/>是不可能直接观察因果效应。然而，这并不使因果推断成为不可能。某些技术和假设可以克服基本问题。
!吝啬的||115||125||−10
!吝啬的||115||125||−10
|}
|}
We can infer what Joe's potential outcome under control would have been if we make an assumption of constant effect:
如果我们假设效应恒定，我们可以推断出乔在控制下的潜在结果是什么：
如果我们假设效应恒定，我们可以推断出乔在控制下的潜在结果是什么：
<math>Y_{t}(u)=T+Y_{c}(u)</math>
<math>Y_{t}(u)=T+Y_{c}(u)</math>
和
和
<math>Y_{t}(u)-T=Y_{c}(u)</math>。
<math>Y_{t}(u)-T=Y_{c}(u)</math>。
If we wanted to infer the unobserved values we could assume a constant effect. The following tables illustrates data consistent with the assumption of a constant effect.
如果我们想推断未观察到的值，我们可以假设一个恒定的影响。下表说明了与恒定效应假设一致的数据。
如果我们想推断未观察到的值，我们可以假设一个恒定的影响。下表说明了与恒定效应假设一致的数据。
!吝啬的||115||125||−10
!吝啬的||115||125||−10
|}
|}
All of the subjects have the same causal effect even though they have different outcomes under the treatment.
所有受试者即使在治疗下有不同的结果，也具有相同的因果效应。
所有受试者即使在治疗下有不同的结果，也具有相同的因果效应。
===分配机制===
===分配机制===
The assignment mechanism
The assignment mechanism, the method by which units are assigned treatment, affects the calculation of the average causal effect. One such assignment mechanism is randomization. For each subject we could flip a coin to determine if she receives treatment. If we wanted five subjects to receive treatment, we could assign treatment to the first five names we pick out of a hat. When we randomly assign treatments we may get different answers.
Assume that this data is the truth:
分配机制，即分配单位处理的方法，影响平均因果效应的计算。一种分配机制是随机化。对于每个受试者，我们可以抛硬币来确定她是否接受处理。如果我们希望五个受试者接受处理，我们可以将处理分配给我们从帽子里挑选出来的前五个名字。当我们随机分配处理时，我们可能会得到不同的答案。
分配机制，即分配单位处理的方法，影响平均因果效应的计算。一种分配机制是随机化。对于每个受试者，我们可以抛硬币来确定她是否接受处理。如果我们希望五个受试者接受处理，我们可以将处理分配给我们从帽子里挑选出来的前五个名字。当我们随机分配处理时，我们可能会得到不同的答案。
|}
|}
The true average causal effect is −8. But the causal effect for these individuals is never equal to this average. The causal effect varies, as it generally (always?) does in real life. After assigning treatments randomly, we might estimate the causal effect as:
真正的平均因果效应是 -8。但是对这些人的因果效应永远不会等于这个平均值。因果效应各不相同，因为它通常（总是？）在现实生活中也是如此。在随机分配处理后，我们可以估计因果效应为：
真正的平均因果效应是 -8。但是对这些人的因果效应永远不会等于这个平均值。因果效应各不相同，因为它通常（总是？）在现实生活中也是如此。在随机分配处理后，我们可以估计因果效应为：
|}
|}
A different random assignment of treatments yields a different estimate of the average causal effect.
处理的不同随机分配产生对平均因果效应的不同估计。
处理的不同随机分配产生对平均因果效应的不同估计。
|}
|}
The average causal effect varies because our sample is small and the responses have a large variance. If the sample were larger and the variance were less, the average causal effect would be closer to the true average causal effect regardless of the specific units randomly assigned to treatment.
Alternatively, suppose the mechanism assigns the treatment to all men and only to them.
平均因果效应会有所不同，因为我们的样本很小并且反馈效应的方差很大。如果样本较大且方差较小，则无论随机分配给处理的特定单位如何，平均因果效应将更接近真实的平均因果效应。
平均因果效应会有所不同，因为我们的样本很小并且反馈效应的方差很大。如果样本较大且方差较小，则无论随机分配给处理的特定单位如何，平均因果效应将更接近真实的平均因果效应。
|}
|}
Under this assignment mechanism, it is impossible for women to receive treatment and therefore impossible to determine the average causal effect on female subjects. In order to make any inferences of causal effect on a subject, the probability that the subject receive treatment must be greater than 0 and less than 1.
在这种分配机制下，女性不可能接受处理，因此无法确定对女性受试者的平均因果效应。为了对受试者做出因果效应的任何推断，受试者接受治疗的概率必须大于 0 且小于 1。
在这种分配机制下，女性不可能接受处理，因此无法确定对女性受试者的平均因果效应。为了对受试者做出因果效应的任何推断，受试者接受治疗的概率必须大于 0 且小于 1。
===完美的医生===
===完美的医生===
The perfect doctor
Consider the use of the perfect doctor as an assignment mechanism. The perfect doctor knows how each subject will respond to the drug or the control and assigns each subject to the treatment that will most benefit her. The perfect doctor knows this information about a sample of patients:
考虑使用完美医生作为分配机制。完美的医生知道每个受试者对药物或对照的反应如何，并为每个受试者分配对她最有益的处理。完美的医生知道有关患者样本的以下信息：
考虑使用完美医生作为分配机制。完美的医生知道每个受试者对药物或对照的反应如何，并为每个受试者分配对她最有益的处理。完美的医生知道有关患者样本的以下信息：
|}
|}
Based on this knowledge she would make the following treatment assignments:
基于这些知识，她将进行以下处理分配：
基于这些知识，她将进行以下处理分配：
!吝啬的||113.75||110||3.75
!吝啬的||113.75||110||3.75
|}
|}
The perfect doctor distorts both averages by filtering out poor responses to both the treatment and control. The difference between means, which is the supposed average causal effect, is distorted in a direction that depends on the details. For instance, a subject like Susie who is harmed by taking the drug would be assigned to the control group by the perfect doctor and thus the negative effect of the drug would be masked.
完美的医生通过过滤掉对处理和控制的不良反应来扭曲这两个平均值。均值之间的差异，即假定的平均因果效应，在取决于细节的方向上发生扭曲。例如，像Susie这样因服药而受到伤害的受试者会被完美的医生分配到对照组，从而掩盖了药物的负面影响。
完美的医生通过过滤掉对处理和控制的不良反应来扭曲这两个平均值。均值之间的差异，即假定的平均因果效应，在取决于细节的方向上发生扭曲。例如，像Susie这样因服药而受到伤害的受试者会被完美的医生分配到对照组，从而掩盖了药物的负面影响。
==结论==
==结论==
Conclusion
The causal effect of a treatment on a single unit at a point in time is the difference between the outcome variable with the treatment and without the treatment. The Fundamental Problem of Causal Inference is that it is impossible to observe the causal effect on a single unit. You either take the aspirin now or you don't. As a consequence, assumptions must be made in order to estimate the missing counterfactuals.
The Rubin causal model has also been connected to instrumental variables (Angrist, Imbens, and Rubin, 1996)[6] and other techniques for causal inference. For more on the connections between the Rubin causal model, structural equation modeling, and other statistical methods for causal inference, see Morgan and Winship (2007).[7]
在某个时间点对单个单位的处理的因果效应是经过处理和未经过处理的结果变量之间的差异。因果推断的基本问题是不可能观察到对单个单元的因果效应。你要么现在服用阿司匹林，要么不服用。因此，必须做出假设以估计缺失的反事实。
在某个时间点对单个单位的处理的因果效应是经过处理和未经过处理的结果变量之间的差异。因果推断的基本问题是不可能观察到对单个单元的因果效应。你要么现在服用阿司匹林，要么不服用。因此，必须做出假设以估计缺失的反事实。