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I have a manufacturing problem with input variable I, intermediate additive A and output O. I have observational data of these variables.

Both I and A can impact O, to some extent. Moreover, A is partly determined by I in the data I have. That is, based on the input level, additive levels are partly determined (there's a trend), but not fully.

O = f(I, A) + error_f, A = g(I) + error_g.

My goal is to find the effect of A on O, for different levels of I.

How to frame it in terms of causal analysis? I tried to read about mediators and moderators, but they do not seem to really fit my problem. Also, it's impossible to perform randomized experiments due to practical reasons, so I am dependent on observational data.

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  • $\begingroup$ What kind of scales have your variables? $\endgroup$
    – POC
    Commented Mar 5, 2021 at 18:15
  • $\begingroup$ they are continuous, positive $\endgroup$
    – learning
    Commented Mar 5, 2021 at 18:23

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If you want to see the effect of A on O at different levels of I then moderation analysis is what you are looking for. The model would be $O=A+I+A*I+e_O$.

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  • $\begingroup$ Thanks. How would this regression equation differ from that for mediation analysis? $\endgroup$
    – learning
    Commented Mar 7, 2021 at 14:45
  • $\begingroup$ A lot actually. see stats.stackexchange.com/a/309386/102655 there is a lot of documentation on this topic. $\endgroup$
    – POC
    Commented Mar 7, 2021 at 17:53

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