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The dataset I have is

  • an aggregated outcome, e.g., the quarterly revenue of each firm (that manages a number of plants), revenue is measured by the end of each quarter
  • a focal explanatory variable, e.g., number of workers reported to each plant each week

Previously, I aggregated the explanatory to the quarterly level so that the outcome and explanatory variables are at the same level. However, one reviewer indicated that I should use a multilevel linear model instead. But, my understanding is appending the end-of-quarter outcome to each weekly observation and study at the weekly level is not the right way to model the above relationship. I am interested in knowing what you think about this and any suggestions (recommended readings) are appreciated.

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  • $\begingroup$ This is actually a causality question. In Simpson's Paradox, e.g., if you have a mediator you SHOULD aggregate the mediator variable. If you have a confounding variable, you should NOT aggregate. The difference is in which way the arrows are pointing in the causal diagram. For more info, see The Book of Why, pages 202ff. $\endgroup$
    – Adrian Keister
    Commented Jun 8, 2021 at 20:35
  • $\begingroup$ Thanks, what if my primary objective is to uncover the relationship (not claiming causality)? Then, can I just simply appending the aggregated outcome to weekly observation to estimate a regression model? $\endgroup$
    – user001
    Commented Jun 8, 2021 at 20:49
  • $\begingroup$ Including a variable in a regression is how you condition on it in the regression setting. That is like not aggregating. It really depends on the causal diagram, which way to go. You will get the wrong answer if you do the wrong thing. The consequences will be more or less severe depending on how strongly the variable you're mis-handling affects the effect. Do you think you could come up with a causal diagram showing how your variables cause each other? Here $A\to B$ is how you would write "$A$ causes $B$." $\endgroup$
    – Adrian Keister
    Commented Jun 8, 2021 at 20:53

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