[R-sig-eco] Multivariate ANOVA/repeated measures

[Dave Roberts]

On 10/07/2011 08:51 AM, Dr N.A. Cutler wrote:
> Dear All,
>
> I have a query about multivariate analysis of community data.
>
> In my experiment, 24 microbial communities in different locations were
> sampled using Sampling Technique 1 (ST1). A site X species matrix was
> then derived by molecular analysis.
>
> The same 24 locations were then sampled again using a different sampling
> technique (ST2) and a second site X species matrix was derived. It is
> assumed that community structure remains intact after sampling by
> Technique 1 i.e. the two techniques can sample from the same pool of
> organisms.
>
> I want to compare the results of the two sampling exercises in order to
> test the performance of the two sampling techniques. My research
> question is: does Technique 1 produce a similar signal to Technique 2?
> Or do the different techniques give significantly different pictures of
> community structure? The null hypotheses is that there is no significant
> difference between the two sampling techniques i.e. they both capture
> community structure with the same degree of accuracy.
>
> It occurred to be that I could use a multivariate ANOVA technique (e.g.
> Adonis) to distinguish between the results of the two sampling
> exercises, using sampling technique as a factor. But I am not sure how
> to deal with the obvious correlation between sample pairs. Should this
> situation be addressed as a repeated measures experiment with two time
> steps? If so, what is the best technique to use (a mixed model, perhaps?)
>
> Any advice would be gratefully received.
>
> Best wishes,
>
> Nick Cutler
>
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Nick,

    I would try something pretty direct.  Any appeal to differences in 
dissimilarities confounds the effects with the particular 
dissimilarity/distance matrix you use.  Assuming the samples and species 
are in the same order, and that the data.frames are the same size, you 
might try

 > actual <- sum((ST1-ST2)^2)

and then permute one of the two matrices numerous times

res <- rep(NA,999)
for (i in 1:999) {
      res[i] <- sum((ST1-ST2[sample(1:nrow(ST2),replace=FALSE),])^2)
}
final <- (sum(res <= actual) + 1)/1000

and see what fraction of the permuted matrices are as similar.

Hopefully Gavin will weigh in with a better randomization.

    If you do go with a multivariate approach I might try a procrustes 
analysis of PCO ordinations.

Dave
-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
David W. Roberts                                     office 406-994-4548
Professor and Head                                      FAX 406-994-3190
Department of Ecology                         email droberts at montana.edu
Montana State University
Bozeman, MT 59717-3460