The Poisson model is probably the first that pops into mind when trying to model count data, which is generally described as: non-negative integer data. The Poisson distribution is defined as modeling the number of counts which occur in a specific time interval.
My question is: What if I model non-negative integer data with a Poisson GLM for which the underlying process is not a count within a specific time interval?
More specifically, what if I want to model successive counts? For example, what if I want to model the number of successive wins for a football club? Or the number of webpages someone visits on a website? The length of the time interval is then determined based on when the (successive) count ends and different for each observation in a dataset, right? Not entirely the same as for the underlying Poisson process I guess... Therefore I hope someone can give some insight into the following subquestions arising from my initial question.
- What if still the Poisson GLM is used in these situations, what will be the consequences?
- If there are consequences do these also hold for the Negative Binomial GLM as this can be defined as a Gamma - Poisson mixture?
- Is a more flexible method such as quasi-poisson more suitable in these cases?
Edit: I was triggered by this post, where the answer mentions that real counts are not necessary, but the linked webpage provides no information on this issue, nor can I find anything while searching the internet.