I am trying to model count data of birds in forest fragments of different size. As the plots in which the surveys were conducted also differ in size among fragments, I would like to add survey plot size as an offset term to convert counts to densities.
As I understand from previous questions on this site this is generally done for poisson models as these have a log link. The GAM model (mgcv package) I am running with family ziP has link="identity". As far as I understand in such cases the offset term will be subtracted from the response, rather than resulting in the desired response/offset rate.
However, when I run the model with the offset term and plot the results it seems to be giving the result I want (I compared the plot for a poisson model with the ziP model).
This is the model I used, whereby Guild reflects different feeding guilds, logArea is the log of fragment size and Study is my random effect (data come from several studies).
gam1 <- gam(Count ~ Guild + s(logArea, by=Guild) + s(Study,bs="re"), offset=lnTotalPlotsize, family=ziP(),data=Data_ommited2)
Can someone explain how GAM handles offset terms in this case (ziP model with identity link)? Is it really resulting in the desired response/offset rate or is it doing something else?
Thanks for your help!
Regards, Robert
Whilst only the identity link is provided, the linear predictor returns the log of the expected count. As such the linear predictor is on a log-scale and your use of the offset is OK.
Basically, the model is parameterized for the log response not the response, hence identity link functions are used. This is the same as for the ziplss() family.