Modeling a poisson distributed count variable divided by uniformly distributed time variable - Cross Validated most recent 30 from stats.stackexchange.com 2019-10-22T01:25:54Z https://stats.stackexchange.com/feeds/question/229327 https://creativecommons.org/licenses/by-sa/4.0/rdf https://stats.stackexchange.com/q/229327 3 Modeling a poisson distributed count variable divided by uniformly distributed time variable Ali Turab Lotia https://stats.stackexchange.com/users/124010 2016-08-11T10:40:59Z 2017-09-16T19:38:46Z <p>We are trying to fit a GLM that estimates the number of insurance claims made in a year using 6 independent variables.</p> <p>The count variables are based on time frames (exposure) so to make it a fair comparison, we divide the count by exposure and call it frequency which gives an estimate of the counts you would expect in year.</p> <p>The count variable follows a poisson distribution and exposure is a uniform distribution between 0 and 1.</p> <p>The residuals vs. fits plot for frequency looks like: <a href="https://i.stack.imgur.com/umIoj.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/umIoj.png" alt="resid vs. fits frequency"></a></p> <p>The problem is that a GLM modeling frequency with a poisson family is returning warnings as it is modeling a count variable and not getting integer values (as count/exposure often returns float values). Rounding the frequency response variable is not an option as it leads to other conceptual problems.</p> <p>Should I ignore the warnings and use the fitted model?</p> https://stats.stackexchange.com/questions/229327/-/303485#303485 2 Answer by kjetil b halvorsen for Modeling a poisson distributed count variable divided by uniformly distributed time variable kjetil b halvorsen https://stats.stackexchange.com/users/11887 2017-09-16T19:38:46Z 2017-09-16T19:38:46Z <p>You should not divide the counts by the exposure, but include the logarithm of exposure as an offset in the model, and then fit a poisson regression with log link function. See <a href="https://stats.stackexchange.com/questions/142338/goodness-of-fit-and-which-model-to-choose-linear-regression-or-poisson/142353#142353">Goodness of fit and which model to choose linear regression or Poisson</a> and <a href="https://stats.stackexchange.com/questions/11182/when-to-use-an-offset-in-a-poisson-regression">When to use an offset in a Poisson regression?</a> for details. </p>