I was catching birds in 2 different areas, each containing 4 sites. Obviously,a site can only be in one area or the other, meaning that the site is nested within area. My effect of interest is the area and not the site. Will I need to treat the nested effect also as a random effect?
i.e will the model be
I would be great if somebody could hel me out of that situation.
This is much more of thought question. The inference space between the two expressions is different. The first infers to the areas and sites only--the inference space is only those areas and sites sampled, answering the question "Is there a difference between these sites, and only these sites?" The latter refers to a broader inference space--that the sites within each area are somehow a random sample of all possible sites, so that you are answering the question, "Is there a difference between these two areas, averaged over all possible sites within an area?" So it comes down to which of these questions is closer to the research question at hand. A good reference for this would be Littel et. al., SAS for Mixed Models, or the online SAS documentation--search on "inference space".