Directed acyclic graphs , su ¢ cient causes and the properties of conditioning on a common e ¤ ect
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چکیده
Su¢ cient-component causes are incorporated into the directed acyclic graph (DAG) causal framework in order to make apparent several properties of conditioning on a common e¤ect. By incorporating su¢ cient causes on a graph, it is possible to detect conditional independencies within strata of the conditioning variable which are not evident on DAGs without the representation of su¢ cient causes. It is also possible to determine the sign of the conditional covariance of two causes when conditioning on their common e¤ect if some knowledge of the su¢ cient cause mechanisms for the common e¤ect is available. The incorporation of su¢ cient causes within the DAG framework also allows for the representation of interactions on DAGs and for the uni cation of several di¤erent causal frameworks. For illustration, the results are applied to an example concerning the familial coaggregation of two disorders.
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