[R] offset in glm

[peter dalgaard]

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 using 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
> 
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> 
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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
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