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So I have data from a number of people on the number of sexual partners they've had in their life so far (self reported, but let's assume they're perfectly accurate for this question). I wanted to see what variables might predict number of sexual partners. As this is count data, I thought Poisson regression would be best. However, because people are all of different ages, does that mean that the "equal observation time assumption" of Poisson regression is violated? If so, would including age as a variable in the regression correct this? Thanks!

Thomas Richardson
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  • Welcome to Cross Validated! If you use as dependent variable the number of sexual partners per unit time (per year, for instance), then no, this issue wouldn't violate the assumptions of the Poisson distribution. However, if you're thinking about using age as an independent variable, that means that you believe that people of different ages have different rates of sexual partner per unit time; in that case, perhaps you should read the comments on [this question](https://stats.stackexchange.com/questions/449572/poisson-distribution-with-variable-average-rate-%ce%bb). – LmnICE Jul 21 '20 at 15:07
  • @LmnICE per unit of time might be a good idea, though hard to do with this data. If I used lifetime sexual partners of people with different "sexual careers" but controlled for age (and make the assumption that time of beginning sexual career is equal) would this be a problem? – Thomas Richardson Jul 21 '20 at 15:48
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    It would violate the underlying assumption of the Poisson model. However I'm not sure to what extent it would do so. You'd have to run it and see if the output makes sense. – LmnICE Jul 21 '20 at 17:37

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If the only issue is differing observation durations for different individuals, then using the duration of observation as an offset term is a standard way to proceed in Poisson models. An offset is a predictor that is forced to have a regression coefficient of 1 in the linear predictor, thus directly correcting the total observed counts for the observation period. So in your case you could use the difference between age and "time of beginning sexual career" as an offset.

I suspect, however, that in this particular application there will be a substantial age dependence in the Poisson rate. That will require a more complicated model, as a simple Poisson model assumes a constant underlying rate.

EdM
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