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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.

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Poisson regression typically applies when we're counting how many times something happens within a period of time, so called "count data." What you're talking about is "waiting time" the between event time. For a. Poisson process the between event time is actually drawn from an exponential distribution ( https://en.m.wikipedia.org/wiki/Exponential_distribution ).

So in summary the waiting time is exponential if and only if, the counts over fixed intervals of time are Poisson.

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  • $\begingroup$ I'd also like to consider the number of visits as well as time between visit. I gather a poisson process is a reasonable path? $\endgroup$ – Michael Colfax Oct 25 '15 at 21:46
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Number of visits looks like a good fit to model with Poisson. Days between visits would be exponential distribution. Id' get the data, plot histograms, fit Poisson and exponential and see if they're good fits.

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  • $\begingroup$ Might be worth mentioning the use of an exposure offset in the poisson. $\endgroup$ – Matthew Drury Sep 30 '15 at 20:03

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