# Single World Intervention Graphs : A Primer

@inproceedings{Richardson2013SingleWI, title={Single World Intervention Graphs : A Primer}, author={T. Richardson and J. Robins}, year={2013} }

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… Expand

#### 21 Citations

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Causal Calculus in the Presence of Cycles, Latent Confounders and Selection Bias

- 2019

We prove the main rules of causal calculus (also called do-calculus) for i/o structural causal models (ioSCMs), a generalization of a recently proposed general class of non-/linear structural causal… Expand

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Even with this extension, ordinary graphical models still fail to capture distinctions between hypothetical superpopulations and observed populations, although potential-outcome models can be adapted to show these distinctions and their consequences. Expand

Summary of relationships between exchangeability, biasing paths and bias

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- European Journal of Epidemiology
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This illustration provides a step-by-step illustration of generalized computation of standardization and inverse probability weighting, as well as the specification of marginal structural models, particularly for time-varying exposures, using a novel hypothetical example. Expand

Mediation analysis for different types of Causal questions: Effect of Cause and Cause of Effect

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Many statistical analyses aim at a causal explanation of the data. When discussing
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typical causal question can be… Expand

A Graphical Description of Partial Exchangeability.

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The utility of single world intervention graphs (SWIGs) and the sufficient component cause model are illustrated and an illustrative example of when partial exchangeability might hold in the absence of complete exchangeability is provided. Expand

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