In modeling claim count data in an insurance environment, I began with Poisson but then noticed overdispersion. A Quasi-Poisson better modeled the greater mean-variance relationship than the basic Poisson, but I noticed that the coefficients were identical in both Poisson and Quasi-Poisson models.
If this isn't an error, why is this happening? What is the benefit of using Quasi-Poisson over Poisson?
Things to note:
- The underlying losses are on an excess basis, which (I believe) prevented the Tweedie from working - but it was the first distribution I tried. I also examined NB, ZIP, ZINB, and Hurdle models, but still found the Quasi-Poisson provided the best fit.
- I tested for overdispersion via dispersiontest in the AER package. My dispersion parameter was approximately 8.4, with p-value at the 10^-16 magnitude.
- I am using glm() with family = poisson or quasipoisson and a log link for code.
- When running the Poisson code, I come out with warnings of "In dpois(y, mu, log = TRUE) : non-integer x = ...".
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