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I have a following picture and the assumption that I can estimate the effect of Treatment on Growth by accounting for dT. However, I'm not sure if Unobserved confounder is actually a confounder - it is NOT related directly to Growth. So should I adjust for dT or for nothing?

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    $\begingroup$ The unobserved confounder is a cause of Treatment and Growth, so it is a confounder. dT is also a confounder by some definitions. See my answer about the definition of a confounder here. $\endgroup$
    – Noah
    Commented Oct 28, 2022 at 16:14

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As Noah points out in a comment, the unobserved confounder is indeed a confounder since it creates a back-door path between treatment and growth. However, the model as presented does not contain a causal path between treatment and growth. Dagitty, which is where I presume your figure is from, will tell you that you can adjust for dT and then treatment and growth are independent: no effect to measure.

If there were an arrow between treatment and growth then yes, the unobserved variable would confound the effect, and it would be enough to control for dT, see attached figure.

DAG adapted from above

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  • $\begingroup$ thank you very much for your explanation! So, now I understood that 1) since there is no causal path between treatment and growth, it's impossible to estimate the influence of one to another 2) therefore, finding an adgustment set doesn't make sense $\endgroup$
    – Maria Li
    Commented Oct 28, 2022 at 11:26
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    $\begingroup$ @MariaLi yes. Or perhaps you could say that the model already assumes that there is no influence and if we accept the model at face value there is no sense in doing an adjustment or even in gathering any data. But since the model suggests an independence between treatment and growth if you adjust for dT you can use this as a check for the model: If you adjust for dT and see an effect clearly different from zero that would imply that the model is wrong somehow. $\endgroup$
    – einar
    Commented Oct 28, 2022 at 11:50
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    $\begingroup$ Not drawing an arrow between two variables is the strongest assumption you can express in a DAG. You either believe in the DAG with no influence or you need a new DAG. $\endgroup$
    – Bernhard
    Commented Oct 28, 2022 at 12:36
  • $\begingroup$ Let me clarify: I was provided with this DAG and cannot change it. $\endgroup$
    – Maria Li
    Commented Oct 28, 2022 at 12:40

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