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  • Is Poisson the correct model here?

    • 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
    Last edited by John Biton; 14 Nov 2020, 20:03.

  • #2
    John Biton I think a regression discontinuity design might be a better analysis here, where you would be comparing the number of likes in the hours immediately preceding and immediately following the move to non-promotion. Doing something like an interrupted time series or difference in difference analysis, you can show a decline, but since the curve should be declining it's hard for me to figure out how you would know that the downward trend is sharper than it would be had you kept promoting it. If you go this route, I think you would still want to look at the hours immediately surrounding the intervention. Plotting the trend might help.

    I think the Poisson process would apply to each panel (i.e., hour), not to the entire time series.

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    • #3
      Hi Tom,

      Thanks for the response!

      A couple of clarifications:

      1.You say that since the curve is declining, it's hard to figure out how you would know if the downward trend is sharper than if you kept promoting it. If you look at the functional form I laid out, isn't this effect just B3? B1 is the slope before non-promotion and B1*B3 is slope after non-promotion.

      2. I guess the level information is interesting, but wouldn't a classic RD not be able to account for the fact that likes/hour are going down anyway? I imagine if I look at the hour before non-promotion and after non-promotion, you'd get less likes in the latter simply because likes/hour decline over time.

      3. Can you clarify what you mean about Poisson process applying to each panel?

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      • #4
        Yes, beta 3 might tell you that the slope changes after the intervention, but you would expect that in the absence of the intervention, right? You are modeling a downward slope and trying to detect whether the intervention accelerated the downward trend. So, what is your benchmark to know whether there was acceleration? Right now, you are using the pre-intervention slope, while stating that the post-intervention slope should exhibit more of a decline because of the nature of the like process (i.e., a downward trend over time). This is where I think plotting and showing us the time series would help. Do you have a different benchmark, like data from before the company instituted the non-promotion feature in which to compare the change in like intercepts and slopes?

        No, it wouldn't. But this is the same issue you run into when trying to interpret beta 3. It would be helpful to see how much the number of likes change in the hours immediately before and immediately after the intervention. Maybe you could compare average change from hour t-2 to t-1 to average change from hour t to hour t+1, assuming the number of likes does not drop exponentially hour to hour near the time of the intervention.

        You are modeling your outcome as Poisson distributed at each panel, not over the entire time series. So it is OK if the mean outcome changes over time.

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        • #5
          I would not expect, in the absence of intervention, for the SLOPE to change after the invention. I would expect the number of likes to monotonically decrease, but at the same rate. These two statements are consistent. For example, if the slope is -5*t, then after the invention the number of likes/hour would be lower (as t is greater). But the slope would be the same.

          Also, the specification is somewhat important. The dependent variable is logged in the equation I'd be running. But same as ^^^: In the absence of an intervention, the slope shouldn't change

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          • #6
            OK, so there is a uniform decline in hourly likes over time? I guess I assumed it would be exponential. Your equation makes sense to me, then. Do the current number of likes influence future number of likes? In other words, are people more likely to like an item if it has a lot of likes, or does the number of likes impact how much an item is promoted on a site?

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