You need weights=Holders to make the 2nd form equivalent to the first (with a
bunch of somewhat annoying and largely irrelevant warnings). This is because 300
claims from 1000 holders is more informative than 3 out of 10 even though the
rate is the same.
-pd
> On 27 Feb 2020, at 19:15 , John Smith <jswhct at gmail.com> wrote:
>
> It is simple to use the provided function glm as fit1 below. However,
> without the offset argument, I tried fit2 below. The reason I used fit2 is
> that (for X as predictors, b the coefficients)
> fit2: log(Claims/Holders) = Xb
> means
> fit1: log(Claims)=Xb + log(Holders)
>
> Obviously the results from fit2 are different from fit1.
>
> Thanks!
> ######################################
> library("MASS")
> ## main-effects fit as Poisson GLM with offset
> fit1 <- glm(Claims ~ District + Group + Age + offset(log(Holders)),
> data = Insurance, family = poisson)
> coef(fit1)
>> coef(fit1)
> (Intercept) District2 District3 District4 Group.L
> -1.8105078329 0.0258681909 0.0385239271 0.2342053280 0.4297075387
> Group.Q Group.C Age.L Age.Q Age.C
> 0.0046324351 -0.0292943222 -0.3944318082 -0.0003549709 -0.0167367565
>
> fit2 <- glm(Claims/Holders ~ District + Group + Age,
> data = Insurance, family = poisson)
>> coef(fit2)
> (Intercept) District2 District3 District4 Group.L Group.Q
> -1.86340418 0.17552458 0.11081521 0.15131076 0.43701544 -0.01530721
> Group.C Age.L Age.Q Age.C
> -0.06033747 -0.31976743 -0.01833841 -0.01694737
>
> [[alternative HTML version deleted]]
>
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com