I'm analysing a dataset from a field survey designed to test how tw types of marine protected areas affect species composition of marine seagrasses, and now struggle how to properly deal with the nested nature of our data.
Our design is a mixed model nested ANOVA (following the terminology in Quinn and Keough 2002), with three factors:
1) Management - fixed factor with three levels (open, closure and park)
2) Site: random factor with a total of 12 levels, nested within 'Management'. For each level of management there are 4 unique 'site' levels.
3) Transect; fixed factor with 3 levels (shallow, mid, reef) which is crossed with 'Management'.
Along each 'Transect' there's seagrass species-level shot count data from ca 10 stations (replicates). Sampling was done 1 time in each station, so there's no repeated measures.
We're trying to test the effects of 'Management', 'Transect' and their interaction on seagrass species composition using PERMANOVA as implemented in the adonis() routine in the vegan package for R. The standard code for a design with a blocked (crossed) random factor would be:
adonis(species ~ management * transect, strata = env$site, data = d)
However, in our case the random factor is nested under the main factor - not crossed with it. As I understand it is possible to constrain the permutations using the 'permutations = how' argument, and then specify a custom permutation design. See, for example, here:
https://groups.google.com/forum/#!topic/davis-rug/N3okDWAEsNM
But I've never worked with customized permutation designs before and struggle to find tutorials, so would really appreciate any form of feedback.
Anyone can provide some advise?
I've also looked into the nested.npmanova() function in the BiodiversityR package. This can properly handle a design like ours with 2 factors (one main, one nested) - but we have 3 factors...
We're also open to instead using the mvabund() routine, i.e. a GLM- rather than distance-based framework, if it can help us properly deal with the nested nature of our random 'site' factor. But so far I've only found examples where it can be used to handle crossed random factors.
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