Predict GLM poisson with offset

Question

I know this is probably a basic question... But I don't seem to find the answer.

I'm fitting a GLM with a Poisson family, and then tried to get a look at the predictions, however the offset does seem to be taken into consideration:

model_glm=glm(cases~rhs(data$year,2003)+lhs(data$year,2003),
offset=(log(population)), data=data, subset=28:36, family=poisson())

predict (model_glm, type="response")

I get cases not rates...

I've tried also

model_glm=glm(cases~rhs(data$year,2003)+lhs(data$year,2003)+
offset(log(population)), data=data, subset=28:36, family=poisson())

with the same results. However when I predict from GAM, using mgcv, the predictions consider the offset (I get rates).

I'm missing something?

Answer 1

It is correct you to get cases instead of rates since you are predicting cases. If you want to obtain the rates you should use the predict method on a new data set having all columns equal to data but the population column identically equal to 1, so to have log(populaton)=0. In this case you will get the number of cases of one unit of population, i.e. the rate.