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 = ...".

Helpful SE Threads per Ben's guidance:

1. Basic Math of Offsets in Poisson regression
2. Impact of Offsets on Coefficients
3. Difference between using Exposure as Covariate vs Offset

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 = ...".

Helpful SE Threads per Ben's guidance:

1. Basic Math of Offsets in Poisson regression
2. Impact of Offsets on Coefficients
3. Difference between using Exposure as Covariate vs Offset