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I want to aggregate a dataset which is Poisson-distributed in which each event that occurs is measured at a different time. The data is transformed into transactional data, aggregated on UserID.

So each user has a sum of each event that happened throughout the total measured time period. Next I want to perform a regression. My question is, can I still perform a Poisson regression or should I perform something else? Example of data is the picture below.

Example data

kjetil b halvorsen
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jmutr
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    The sum of independent Poissons is Poisson, but a sum of dependent Poissons might also be Poisson (with the right forms of dependence). It may be that a Poisson will be a reasonable approximation to the conditional distribution of the counts that you have.. – Glen_b Dec 04 '19 at 01:39
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    @Glen_b Can you give an example of dependent Poissons whos sum is Poisson? Their existence seemssomewhat contradiced by jbowman comment here https://stats.stackexchange.com/questions/22179/dependent-thinning-poisson-process – kjetil b halvorsen Dec 27 '19 at 17:32
  • Sorry to give you the wrong impression. I wasn't claiming to know of the existence of such a result; rather I was trying to point out that in a statement of the form "if the Poissons are independent, their sum is Poisson" that the "if" was not necessarily an "iff"; and in any case that makes no direct claim about conditional distributions. My comment in the second sentence about conditional distributions included the phrase "may be [...] a reasonable approximation", so there's no actual claim of any actual Poisson result in that part either. – Glen_b Dec 27 '19 at 22:21
  • jbowman's comment about the restricted form of such dependence at the end is certainly correct (that the correlation must be 0). – Glen_b Dec 27 '19 at 22:53

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