[R] Vegan R^2 and tau values for metaMDS
Gavin Simpson
gavin.simpson at ucl.ac.uk
Mon Apr 14 23:24:48 CEST 2008
On Mon, 2008-04-14 at 17:00 -0400, Sarah Goslee wrote:
> On Mon, Apr 14, 2008 at 4:47 PM, Gavin Simpson <gavin.simpson at ucl.ac.uk> wrote:
>
> > Note that the default is to produce a bray-curtis dissimilarity matrix
> > from the input species data. As such, I reproduce this dissimilarity
> > matrix as arg 1 to cor and then take the Euclidean distances of the
> > coordinates on nMDS axes 1:2 (this example is a 2D solution but scales
> > to n-dimensions) as the second argument to cor:
> >
> > cor(vegdist(dune), dist(sol$points))^2
> >
> > In this example, the "R^2" is 0.899222
> >
> > If you already have jaccard for your species data, then substitute this
> > for 'vegdist(dune)' and sol for whatever your nMDS object is called.
>
> Good point. I forgot to clarify that you should use the same dissimilarity
> metric for your original data that was used in constructing the ordination.
> Euclidean distances should be used for the NMDS configuration, though.
Yes - here I use dist(sol$points) which defaults to Euclidean distances.
>
> > However, this assumes a linear relationship between the original
> > distances and the nMDS distances. The relationship need not be linear,
> > just monotonic if I recall the details correctly.
>
> If you (the original querent) are interested in the monotonic rather than
> strictly linear relationship, you could use the "spearman" option to
> cor().
I forgot about that, thanks for the reminder Sarah. This correlation
(using method = "spearman") is different to the ones used in stressplot.
I peeked inside the code of that function and the following should
reproduce the linear fit R^2 shows on the plot produced by stressplot:
## continuing the example from my previous email
require(MASS) # for Shepard()
shep <- Shepard(vegdist(dune), sol$points)
cor(shep$y, shep$yf)^2
The last line yields = 0.9250712.
The non-metric fit is 1 - stress and this can be calculated using:
1 - (sum((shep$y - shep$yf)^2)/sum(shep$y^2))
So now you have 4 different R^2 values to choose from Stephen...
HTH
G
>
> Sarah
>
--
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Dr. Gavin Simpson [t] +44 (0)20 7679 0522
ECRC, UCL Geography, [f] +44 (0)20 7679 0565
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