I have seen evidence that Poisson regression can be run with either offsets or weights for time and both give the same results. However, I have noticed that the same is not true for Tweedie. I have some sample code below. Can someone tell me why they aren't the same for Tweedie? In addition, I'm guessing the offset is the more appropriate approach, but would like to know for sure. This question was asked before here Offset vs weigths in GLM, but all of the answers related to Poisson, not Tweedie. I would like Tweedie-specific answers, unless it can be shown that they are somehow equivalent.
library(statmod)
library(insuranceData)
data(dataCar)
fit1 <- glm(claimcst0~veh_value+veh_body+veh_age+gender+area+agecat, data=dataCar, offset=log(exposure), family=tweedie(var.power=1.6, link.power=0))
summary(fit1)
fit1a <- glm(claimcst0/exposure~veh_value+veh_body+veh_age+gender+area+agecat, data=dataCar, weight=exposure, family=tweedie(var.power=1.6, link.power=0))
summary(fit1a)
Code originally taken from https://towardsdatascience.com/insurance-risk-pricing-tweedie-approach-1d71207268fc
