A colleague used model averaging in R (MuMIn) for negative bionomial GLM predictions of number of organisms per unit effort: first, including effort as an offset, with count of animals as the response; second, including count of animals per unit effort rounded to the nearest integer as the response (no offset). Should we expect the relative difference between predicted factor levels to be similar for these models? Although generally similar, there were some quite large differences in relative values for the levels of one factor in particular (see attached image, difference between factor levels A and B), and we were wondering what might be the statistical reason for this and if anyone had any similar experience or references on this topic? Thanks in advance.