Solved – Predict GLM poisson with offset

generalized linear modeloffsetpredictionr

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?

Best Answer

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.

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