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I've been told my model wasn't statistically correct, but I'm not sure what I should do.

What I have is basically 2 species: A and B. For each species, I have 3 replicates: 1, 2, and 3 (=6 populations in total). I'm applying a treatment with 3 levels to each population (with different individuals being used for different treatment levels). And I'm testing the effect of the species, the treatment and of their interaction on the response variable.

I therefore need to nest my replicated populations within 'species', as I am interested in the 'species' effect.

The model I wrote was:

model <- lmer(response variable ~ treatment*species + (1|population), data=data)

with 'population' being the combination between 'species' and 'replicate', and therefore each species has 3 distinct levels of population (A1, A2, A3 and B1, B2, B3).

This should thus be equivalent to:

model <- lmer(response variable ~ treatment*species + (1|species:replicate), data=data)

So I thought the nesting was OK like this. But I got the complaint that, because I have a split-splot design, I should include the treatment*replicate(species) interaction in the model, so that populations are treated as the appropriate unit of replication.

Am I missing something, or is my model already correct with this lmer specification? As I have already nested replicate within species, I thought it was taken care of.

Thanks!

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  • $\begingroup$ Unless there's something I don't understand, I don't think you have any nesting here... you should just do either an ANOVA or regression with dummy codes. $\endgroup$ Apr 24, 2014 at 18:57
  • $\begingroup$ Thanks Patrick! I am interested in the species differences, and I tested several populations of each species in my experiment. However, I am not interested in the 'population' effect, I just want to look at the 'species' effect. By specifying my model like I did, I think I've nested 'replicate' (or 'population') within 'species'. Didn't I? $\endgroup$
    – Hal
    Apr 24, 2014 at 19:03

1 Answer 1

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Without more information about the study design it is hard to know for sure, but if this is really a split-plot design (and only you can know that because it is a feature of the study design, not the data or the model) then your original model looks correct

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