I am hoping you can give me some advice about when to use fixed and random effects model. I am currently working on a paper that examines the effect of . . . by comparing states . . .
It got reviewed . . . by three economists and all suggest that we run a fixed effects model. We ran a hierarchial model in the paper that allow the intercept and slope to vary before and after . . . My question is which is correct? We have ran it both ways and really it makes no difference which model you run, the results are very similar. But for my own learning, I would really like to understand which to use under what circumstances. Is the fact that we use the whole population reason enough to just run a fixed effect model?
Perhaps you can suggest a good reference to this question of when to run a fixed vs. random effects model.
I’m not always sure what is meant by a “fixed effects model”; see my paper on Anova for discussion of the problems with this terminology:
Sometimes there is a concern about fitting multilevel models when there are correlations; see this paper for discussion of how to deal with this:
The short answer to your question is that, no, the fact that you use the whole population should not determine the model you fit. In particular, there is no reason for you to use a model with group-level variance equal to infinity. There is various literature with conflicting recommendations on the topic (see my Anova paper for references), but, as I discuss in that paper, a lot of these recommendations are less coherent than they might seem at first.