Suppose a particular gym has asked you to tell them about their gym members, specifically the gym members' use of the gym. And suppose they supply you with data describing a sample of gym members' usage of the gym within the last few weeks in the form of counts and the time between each gym visit in days. Something like this:
Visit | Member | Time since last visit 2 1 3 1 1 0 4 2 1 3 2 5 2 2 9 1 2 0 1 3 0 3 4 8 2 4 2 1 4 0
... and so on. Suppose other descriptors as well, like gender, age, etc.
You would like to tell the gym about differences in time between usage in sex, and comment on how the younger gym members use the gym more frequently (youth and all its vigor and what not...who knows I'm no scientist).
How would you chose to model these data? Poisson, or maybe a variant?
Your discussion is very much appreciated.