I know that for poisson regressions on count data that originate from different sampling "sizes", i.e. different volumes, areas etc, require an offset in order to adjust for the different sizes.
However, in Zuur et al. (2009) Mixed Effects Models in R in read on page 198 (ch.8.3.1.)
One option is to use the density Ni/Vi as the response variable and work with a Gaussian distribution, but if the volumes differ considerably per site, then this is a poor approach as it ignores the differences in volumes.
In my case, I have counts of harbor porpoise sightings on different sized areas. But, the counts were transformed to densities. Yet, the areas on which the densities were calcualted from are very different.
My Question now: Can I use an offset for a continous response (actually I use the tweedie distribution since I have more than 60% zeros in the data).
One additonal thing: I compared models with offset and without using AIC. The one with the
offset(log(area+1)) was "best".