Causal Diagrams for Empirical Research

Causal Diagrams for Empirical Research

1994 | Pearl, Judea
The paper by Judea Pearl introduces a principled, nonparametric framework for causal inference using graphical models. The primary aim is to show how these models can integrate statistical and subject-matter information to determine if available assumptions are sufficient for identifying causal effects from non-experimental data. If so, the models can produce mathematical expressions for causal effects in terms of observed distributions; otherwise, they can suggest additional observations or experiments to achieve this. The paper begins with an example from agricultural experiments, where the goal is to assess the total effect of fumigants on oat crop yields, considering confounding factors such as eelworm populations and bird populations. The method involves constructing a causal diagram to represent the investigator's understanding of the causal influences among the variables. The diagram is then used to query whether the assumptions are sufficient for consistent estimation of the causal effect and to derive the effect if possible. The paper defines the formal semantics of causal diagrams, including their use in representing conditional independence assumptions and causal influences. It introduces the concept of d-separation to determine the set of all independencies implied by a given decomposition. The diagrams are also interpreted as models of intervention, where external interventions can be represented as alterations to the model, and the effects of these interventions can be derived. The paper discusses the back-door and front-door criteria for controlling confounding bias in observational studies. The back-door criterion involves selecting a set of variables that blocks all paths from the treatment to the outcome, while the front-door criterion involves using a mediating variable to adjust for confounding factors. These criteria provide graphical conditions for identifying causal effects from non-experimental data. Finally, the paper presents a symbolic calculus for deriving causal effect formulas step-by-step, using inference rules that transform probabilistic sentences involving actions and observations into equivalent sentences. This calculus facilitates the derivation of causal effects in complex causal diagrams and provides a systematic method for assessing the identifiability of causal effects.The paper by Judea Pearl introduces a principled, nonparametric framework for causal inference using graphical models. The primary aim is to show how these models can integrate statistical and subject-matter information to determine if available assumptions are sufficient for identifying causal effects from non-experimental data. If so, the models can produce mathematical expressions for causal effects in terms of observed distributions; otherwise, they can suggest additional observations or experiments to achieve this. The paper begins with an example from agricultural experiments, where the goal is to assess the total effect of fumigants on oat crop yields, considering confounding factors such as eelworm populations and bird populations. The method involves constructing a causal diagram to represent the investigator's understanding of the causal influences among the variables. The diagram is then used to query whether the assumptions are sufficient for consistent estimation of the causal effect and to derive the effect if possible. The paper defines the formal semantics of causal diagrams, including their use in representing conditional independence assumptions and causal influences. It introduces the concept of d-separation to determine the set of all independencies implied by a given decomposition. The diagrams are also interpreted as models of intervention, where external interventions can be represented as alterations to the model, and the effects of these interventions can be derived. The paper discusses the back-door and front-door criteria for controlling confounding bias in observational studies. The back-door criterion involves selecting a set of variables that blocks all paths from the treatment to the outcome, while the front-door criterion involves using a mediating variable to adjust for confounding factors. These criteria provide graphical conditions for identifying causal effects from non-experimental data. Finally, the paper presents a symbolic calculus for deriving causal effect formulas step-by-step, using inference rules that transform probabilistic sentences involving actions and observations into equivalent sentences. This calculus facilitates the derivation of causal effects in complex causal diagrams and provides a systematic method for assessing the identifiability of causal effects.
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