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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 season within 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 (1|Site) instead.

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?

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  • $\begingroup$ If somebody suggests you to nest season within site, why don't they suggest to nest color within site as well? From your description, it sounds like color and season are in the same relationship with site. Another question: for each color-site-season combination, do you have 1 abundance measurement, or more? $\endgroup$ – amoeba Jul 22 '17 at 22:31
  • $\begingroup$ They also suggested nesting "color" but they were less sure about that. For each color-site-season combination there is only one abundance measurement. I don't understand why i would need to nest season and abundance within site. to me they look like they are crossed not nested within site. $\endgroup$ – rhomboideus capitis Jul 22 '17 at 23:25
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    $\begingroup$ Yes, they are crossed. However, color and season are repeated measures on each (random) site. To mimic in lmer what classical repeated-measures ANOVA is doing to analyze this design, one needs to include (1|site) and also (1|site:season) which together are equivalent to (1|site/season). The idea is that each site can have its own random deviation from the rest but also each site-season combination can have its own random deviation as well. In mixed models logic, it is much more common to use (season|site) approach. $\endgroup$ – amoeba Jul 23 '17 at 7:56
  • $\begingroup$ [cont.] The full model in your case would be color*season+(color+season|site). But one can choose to use a simpler model color*season+(1|site); recommendations differ. $\endgroup$ – amoeba Jul 23 '17 at 7:57
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    $\begingroup$ Thank you, this was very helpful. i found this wonderful site which shows how to replicate what aov does with lme and lmer. i'll put it here just in case someone in the future needs it dwoll.de/rexrepos/posts/… $\endgroup$ – rhomboideus capitis Jul 23 '17 at 22:57

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