Does a constant offset term meaningfully influence Poisson GLM? If my offset term is a constant value, does this change the outcome of a Poisson GLM regression?
I have survey count data that we summarize as a rate (Counts/Area-Surveyed). In this case, transect area is a constant (60m^2). Some brief exploration of my data suggests that estimated coefficients are different between the two models below, but that p-values do not differ significantly.
m1 = glm(counts ~ group)
m2 = glm(counts ~ group + offset(log(area.surveyed))) ##  area.surveyed = 60 for all observations
Is there any point to using an offset when it is the same value for all observations? My intuition is that I should leave out the offset and just model counts.
sort of similar question here
another offset question here

The offset allows us to directly model rates, not counts. The inclusion of an offset terms thus strongly depends on our application and/or research question.
Even if the offset is "the same value for all observations" it makes sense to include it if we want our coefficients to express changes in rates against a standardised population size. Similarly, it is only natural that if we assume that that the offset values are effectively equal, for the statistical significance of our coefficients to remain effectively unchanged too. That said, if there is a well-defined unit of measurement, omitting the offset might might indeed make our results easier to interpreter. Finally, coming to the particular example mentioned: if I read the results of a survey where the transect area was 60 sqm but was not included in the offset I would be a bit annoyed as I wouldn't know how they would easily compare to the results of another survey what use 50 sqm or 75 sqm....
