• I have data on a company who instituted a feature where they stop promoting items listed after X hours. And they are interested in how that non-promotion affects the amount of "likes" on an item. The hypothesis is that it decreases them
  • But the thing is, likes already decrease over time anyway. So we really want to compare slopes before and after non-promotion, where dependent variable is likes per hour
  • Assume we can't do a controlled experiment
If likes per hour are a poisson process, I'd do this:

𝑙𝑜𝑔(𝑦_t)=α+𝛽1𝑇 + 𝛽2𝑋+ 𝛽3𝑋*𝑇+ε

where 𝑦_t = likes in specific hour, 𝑇 = hour since initially posted, 𝑋 = indicator variable for after X hours (so promotion stops) and 𝑋*𝑇 = time since posted * Is after X hours.

And 𝛽1 vs 𝛽3 compares the relative slopes (for log likes) before and after non-promotion.

Does this make sense?

The thing, is I thought that a Poisson process is one where the mean is the same at each time period. But I definitely know the mean number of likes per hour differs by time period