The standard way to parameterize the distributions represented by a directed acyclic graph is to insert a parametric family for the conditional distribution of each random variable given its parents. We show that when one's goal is to test for or estimate an effect of a sequentially applied treatment, this natural parameterization has serious deficiencies. By reparameterizing the graph using structural nested models, these deficiencies can be avoided.
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Robins et al. (2013) studied this question.
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