3
$\begingroup$

We are trying to fit a GLM that estimates the number of insurance claims made in a year using 6 independent variables.

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.

The count variable follows a poisson distribution and exposure is a uniform distribution between 0 and 1.

The residuals vs. fits plot for frequency looks like: resid vs. fits frequency

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.

Should I ignore the warnings and use the fitted model?

$\endgroup$
2
$\begingroup$

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 Goodness of fit and which model to choose linear regression or Poisson and When to use an offset in a Poisson regression? for details.

$\endgroup$
  • 1
    $\begingroup$ I agree with Kjetil's comments. However, the OP does not state the unit of analysis. Is it at the cohort level? Household? Individual claimant? Health insurance claims are well known not to fit GLM assumptions as they are too extreme valued with 5%-10% of claimants accounting for an enormous percentage of both the number of claims and payout. Negative binomial models are a better choice than Poisson. An even better fit can be had from a nonparametric and robust approach such as quantile regression. Once the quantiles are defined, then any distribution can be used to explain the process. $\endgroup$ – Mike Hunter Sep 16 '17 at 19:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.