# Can you use the Poisson GLM if there is an upper limit?

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?

• 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? – Alejandro Ochoa Aug 18 '16 at 16:10

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.