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 <jsw...@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]] > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.