Before I go into my question I'd like some clarification on fixed and random effects. From what I understand "Effects are fixed if they are interesting in themselves or random if there is interest in the underlying population". So the variable "teachers" would be a fixed effect if I care about particular teachers but a random effect if I care about teachers in general. Is that correct? Keep in mind I'm working in Ecology and strict statistical definition will probably be lost on me.
My real question is whether I should nest some groups within my study. I have 3 categorical variables "site", "season", "bowl color" and a response/dependent variable "abundance". "Site" is set as a random effect. Abundance was measured repeatedly at each site during each season. And bowls of each color were placed in all sites during each season. It does not seem to me like any of my groups should be nested within another. However it was suggested to me that I might need to nest
site. Is this correct?
In R my model is:
lmer(Abundance ~ Seasons + Color + (1|Site/Seasons), data=data)
I'm thinking I should just use
From what I understand in a mixed model group A should be nested within group B if certain categories in group A are only found in certain categories of group B. For example "teachers" would be nested within "school" if some teachers only teach at one school, so teachers 1-5 only teach at school1, teachers 6-10 only at school2 etc... If all teachers teach at all the schools than group A should not be nested within group B, is that correct?
Also the example in this link seems to contradict my understanding: http://www.jason-french.com/tutorials/repeatedmeasures.html. It seems to me like the groups should not be nested but the authors nest them anyway. Is it wrong or am I missing something?