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I've got a problem while trying to specify the 'right' nesting of the random effects of my dataset. The dataset registers hourly variations in temperature inside termite mounds:

  1. Sampling was performed in four localities, differing in soil composition.
  2. On each locality, ~20 termite mounds were sampled.
  3. The temperature of each termite mound was registered every hour during a day.

So, 24 data, per mound, in four localities. According to this previous question, to study how temperatures changes within mounds and among localities, I drew my model as:

Tmodel <- lmer(Temperature ~ Hour + Locality + (1|Locality/Mound/Hour), Tver, REML=FALSE)

and I got this message: 

Error in checkNlevels(reTrms$flist, n = n, control) : 
number of levels of each grouping factor must be < number of observations

From this message, I get that I'm sort of 'constraining' my data, so that per grouping factor (hour, in mound, in locality), there is just one observation; am I right? But then, how should I specify the nestedness of my random factors?

amoeba
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Antón David Pérez Rodríguez
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    What is "locality"? Are you interested in differences between localities (do you have a priori hypotheses about what these differences might be?), or is it just increasing your sample size from 20 mounds to 80 mounds? – amoeba Jun 14 '17 at 20:42
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    Hi, amoeba, thanks for the input. The four localities in which the termite mounds were sampled differ in soil composition, what ultimately could modify the thermoregulatory properties of the mounds. So 'yes', we had the a priory hypothesis that "Locality" would affect mound temperature. – Antón David Pérez Rodríguez Jun 14 '17 at 20:47
  • OK. Then locality is a fixed effect, as well as hour. You have only one random effect - mound, and so you don't have any "nested random effects" at all. Try `Temperature ~ Hour + Locality + (1|Mound)`. This formula assumes that `Mound` is coded such that mounds from different localities have different ids. If this is not the case (e.g. you have mounds 1 to 20 in locality #1 and then again mounds 1 to 20 in locality #2), then you should use `Temperature ~ Hour + Locality + (1|Locality:Mound)`. – amoeba Jun 14 '17 at 20:52
  • (And it would probably make more sense to model the dependency on `Hour` via polynomials or splines, taking its circular nature into account, but this is another issue.) – amoeba Jun 14 '17 at 20:56
  • Thank you very much by the interest you're taking in my problem. I get now that 'Locality' could be considered a fixed factor, but still... I don't see it clear: I'm using mixed models to account for the longitudinal nature of the hourly data. Then, I cannot see how my dataset is conceptually different of that of 'sleepstudy' (http://lme4.r-forge.r-project.org/lMMwR/lrgprt.pdf - page 57 onwards). There, days are nested within subjects (Days|Subject), so why shouldn't I nest hours within termite mounds (Hour|Mound)? – Antón David Pérez Rodríguez Jun 15 '17 at 08:43
  • Let's use correct terminology: in the `sleepstudy` data days are NOT nested in subjects (and I don't think your link says it); days are repeated measures within subjects. But you are right that it's similar to your situation. So you can use either (1|Mound) or (Hour|Mound); the first option is random intercept, the second is random intercept and "slope". It's fine to use random slopes, but I would a bit worried that it might not work in your case, because your `Hour` is categorical variable with 24 levels, so (Hour|Mound) would estimate 24 variance parameters and [cont.] – amoeba Jun 15 '17 at 11:49
  • [cont.] 24*23/2=276 correlation parameters which is A LOT, and you don't have enough data to estimate all of that. In contrast, in the sleep study, `Days` is a continuous variable so (Days|Subject) estimates only one random intercept, one random slope, and one correlation between them. – amoeba Jun 15 '17 at 11:50
  • Again, thanks for your fast help. Sorry for the misuse of 'nestedness' regarding the sleepstudy dataset, my bad. You've been more than helpful. – Antón David Pérez Rodríguez Jun 15 '17 at 12:56

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