[R-sig-eco] PERMANOVA and adonis: trying to clear my confusion

[Steve Brewer]

Pedro,

Just to clarify, the approach that I’m advocating (centroidmatrix) comes directly from what Anderson describes in Primer + Permanova (2008) manual for dealing with split-plot designs (which are a type of nested design, pp. 62-64). My understanding of what is done in adonis/adonis 2 is that nesting is handled using the strata function. This randomization restriction could change the p-value of a test, but I don’t think it changes the fact that adonis is using the residual error term to test all effects in the model (somebody correct me if I am wrong about that). Maybe that is a reasonable approach, but that is not how I learned how to do nested, split-plot, and repeated measures using an Expected Means Squares approach, which I believe requires the use of different error terms to test different effects.

I mention this because in your second message you mention differences based on the df of the tests. The randomization restriction, by itself, is not going to affect the error df of the test, only the p-value. Perhaps someone out there does know the answer, but I have personally not found any model statement that will allow one to use anything but the residual error term to test effects using adonis.

Incidentally, nested.npmanova (BiodiversityR implemented through adonis) uses two different error terms to test effects, which in my opinion is a valid approach, but its use is restricted to those simple cases in which you have a whole/sub/residual nested arrangement (i.e., no crossing of factors and thus no interactions).

Steve


Stephen Brewer
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 Brewer web page - https://jstephenbrewer.wordpress.com
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On Jan 8, 2019, at 11:54 AM, Pedro Neves <pedro.neves using oom.arditi.pt<mailto:pedro.neves using oom.arditi.pt>> wrote:

On 08/01/19 14:01, Steve Brewer wrote:
Pedro,

In my opinion, the problem is that adonis can only use the residual error to test effects. It doesn’t matter what formula you use, it simply does not account for random effects.

You will need to break up the analysis into two separate analyses, wherein the tests of season and habitat are based on a matrix of centroids for each location and the test of location is done with the original species matrix.

Hi Steve:

Thanks for your input and for the "centroidmatrix" - I'll check it out. However I believe one should be able to conduct the analysis with my design using adonis/adonis 2. I say this based on the documentation of the functions (because the code is based on the original algorithm of Anderson and because there's one example of using a nested). I think it's just a matter of finding out how to restrict the permutations within Habitats (in my case).

I think the example for the nested design on the Vegan documentation is not very clear (also judging for the amount of times related questions pop up on the internet...) and I'd love to be able to learn how to conduct this analysis properly with R and Vegan and then contribute with more documentation that might help others...

So, if anyone on the list could point me some hints....

All the best:

Pedro



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