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I'm analyzing social network data where roughly 10 groups of 100 people are split into different sized teams. (For example, there are 10 schools, but some of the schools have 5 "classrooms" while other schools have "15 classrooms")

Let's say each student is a node. I'm interested in the number of distinct classrooms that each student interacts with in a week. In particular, I'd like to model the effect of # of teams on the # of distinct classrooms interacted with.

I was thinking about using the poisson family for a generalized linear function. (I thought poisson was appropriate because it is count data over a limited amount of time.)

However, I realize that there is a natural upper limit. No student can interact with more classrooms than are present at their school. Could I still use the poisson and take this into account?

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  • $\begingroup$ I have the same question :(. I understand that in your example there is a upper limit for your outcome, but how would the computer know this? To the computer its just data, and of course there will be a maximum but it has no concept of what this variable is or what the theoretical upper bound is. Have you tried fitting both types of models and seeing the difference? $\endgroup$ – Alejandro Ochoa Aug 18 '16 at 16:10
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In practice, there is always an upper limit ... thats not the point, really. If your count is never close to the upper limit, a poisson regression should be fine. Otherwise maybe logistic regression, that is an binomial model. Remember the poisson limit to the binomial distribution? If the upper limit $n$ is large and probability $p$ is small, the poisson is a good approximation to the binomial. If that is the situation, go along with the poisson model. Otherwise, think binomial.

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