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

Gavin Simpson gavin.simpson at ucl.ac.uk
Tue Oct 11 00:11:10 CEST 2011


On Mon, 2011-10-10 at 15:32 -0600, Dave Roberts wrote:
> 
> On 10/10/2011 02:15 PM, Gavin Simpson wrote:
> > On Mon, 2011-10-10 at 09:11 -0700, Rich Shepard wrote:
> >> On Mon, 10 Oct 2011, Dave Roberts wrote:
> >>
> >>>> I want to compare the results of the two sampling exercises in order to
> >>>> test the performance of the two sampling techniques.
> >>
> >>>    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
> >>
> >>     I did not read the original message, so I hope you'll allow me to join the
> >> thread. My recommendation is to use univariate tree models, particularly a
> >> classification tree (for ordinal explanatory variables; i.e., ST1 and ST2).
> >
> > But the response here is *multivariate* - of course, one could use Glen
> > De'Ath's multivariate regression trees (despite the name it is really a
> > constrained clustering/classification) - but I think there are better
> > ways of solving this particular problem. And unless one has many 100s of
> > observations, the model will need some sort of variance reduction
> > applied (via bagging, or some such) as the one fitted model is
> > potentially highly unstable.
> >
> > G
> >
> >>     This is fully, carefully, and non-technically explained in Chapter 9
> >> (particularly Sections 9.3 and 9.4) in Zuur, Ieno, and Smith "Analysing
> >> Ecological Data." For that matter, I highly recommend reading the whole
> >> book.
> >>
> >> Rich
> >>
> >> _______________________________________________
> >> R-sig-ecology mailing list
> >> R-sig-ecology at r-project.org
> >> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
> >
> 
> It would be fairly simple to boil down to a univariate question.  You 
> could do something as simple as a paired t-test of plot-level species 
> richness or the number of individuals sampled (to compare sampling 
> efficiency), but I still don't see an independent and a dependent variable.
> 
> Dave

Indeed, but species richness is quite a different "comparison" of the
two sampling strategies. The original Q was quite broad so might be what
the OP wants.

The predictor would be the sampling strategy I guess - can you
explain/cluster the data on the basis of sampling strategy?

Compositionally, adonis() would seem to be an appropriate technique here
- it would be effectively a multivariate t-test - and would test if the
multivariate centroids of the species compositions in the two samples
are similar or not (difference of centroids is 0). Of course, if that
Null is rejected, you must test if the difference in centroids is due to
a difference in multivariate dispersions (the spread of the points about
the centroid), which can be done via betadisper().

The issue I'm still thinking about is the permutation - at first look,
your randomisation seems appropriate, especially if the two sampling
strategies can be considered random sampling methods - i.e. all sites
have equal chance of being selected, /and/ that there is no underlying
clustering in the population that should be respected.

The Null hypothesis seems to be that ST1 and ST2 are just two random
samples of some population of species composition/samples that would
arise if you did lots of sampling using ST2.

G

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