Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality
Single World Intervention Graphs ( SWIGs ) : A Unification of the Counterfactual and Graphical Approaches to Causality
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单一世界干预图（SWIG）：反事实和图形因果关系方法的统一
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
T. Richardson
中科院分区：
文献类型：
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作者：
T. Richardson
我们提出了一个简单的图形理论统一因果有向无环图（dag）和潜在的（aka反事实）结果通过节点分裂变换。我们引入了一个新的图，单世界干预图（SWIG）。SWIG编码与治疗变量集上的特定假设干预相关的反事实独立性。SWIG上的节点是相应的反事实随机变量。我们用一些例子来说明这个理论。我们的swg图解理论可以用来推断Robins（1986, 1987）的反事实模型所隐含的反事实独立性关系。此外，在没有隐变量的情况下，识别了反事实的联合分布；识别公式为（Robins et al., 2004）中引入的扩展g计算公式。虽然Robins（1986, 1987）没有使用dag，但我们翻译了他的代数结果，以促进对这一先前工作的理解。罗宾斯方法的一个吸引人的特点是，它在很大程度上避免了做出实验上无法检验的反事实独立性假设。作为一个重要的说明，我们重新审视罗宾斯的g计算的批评（Pearl, 2009，第11.3.7章）；我们使用swg来表明Pearl的所有主张要么是错误的，要么是基于误解。我们还表明，形式主义的简单扩展可用于适应动态制度，并制定非参数结构方程模型，其中在总体水平上制定了与缺乏直接影响相关的假设。最后，我们表明，我们的图形理论也自然地出现在一个扩展的因果贝叶斯网络的背景下，在这个网络中，我们能够在干预之前观察变量的自然状态。
We present a simple graphical theory unifying causal directed acyclic graphs (DAGs) and potential (aka counterfactual) outcomes via a node-splitting transformation. We introduce a new graph, the Single-World Intervention Graph (SWIG). The SWIG encodes the counterfactual independences associated with a specific hypothetical intervention on the set of treatment variables. The nodes on the SWIG are the corresponding counterfactual random variables. We illustrate the theory with a number of examples. Our graphical theory of SWIGs may be used to infer the counterfactual independence relations implied by the counterfactual models developed in Robins (1986, 1987). Moreover, in the absence of hidden variables, the joint distribution of the counterfactuals is identified; the identifying formula is the extended g-computation formula introduced in (Robins et al., 2004). Although Robins (1986, 1987) did not use DAGs we translate his algebraic results to facilitate understanding of this prior work. An attractive feature of Robins’ approach is that it largely avoids making counterfactual independence assumptions that are experimentally untestable. As an important illustration we revisit the critique of Robins’ g-computation given in (Pearl, 2009, Ch. 11.3.7); we use SWIGs to show that all of Pearl’s claims are either erroneous or based on misconceptions. We also show that simple extensions of the formalism may be used to accommodate dynamic regimes, and to formulate non-parametric structural equation models in which assumptions relating to the absence of direct effects are formulated at the population level. Finally, we show that our graphical theory also naturally arises in the context of an expanded causal Bayesian network in which we are able to observe the natural state of a variable prior to intervention.
影响因子：
2
作者：
ROBINS, J
通讯作者：
ROBINS, J