[R-sig-eco] vegan: envfit (vectorfit)

[Gavin Simpson]

On Tue, 2009-09-15 at 17:02 +0200, gabriel singer wrote:
> Hi vegan-users and programmers,
> 
> Can anybody tell me how the function vectorfit (envfit) computes arrow 
> lengths (as fits of a metric variable onto an ordination) exactly? I 
> understand the scaling bit in the end, but have troubles to understand 
> how actually the direction and strength of gradient of the environmental 
> variable with the ordination is identified. Obviously it´s not a mere 
> correlation between the environment variable and ordination scores, as 
> is usually done for a PCA for example (the "loadings" as opposed to the 
> eigenvectors).

It is a least squares fit of the following form:

Y ~ scores1 + scores2

where Y is the vector or matrix of numeric variables you wish to have
vectors for, and scores1 and scores2 are the user-selected axes of the
ordination configuration. If Y is a matrix then each variable (column)
in that matrix enters as a separate regression.

Effectively, it uses the locations of the points (sites) in the selected
2D ordination space to predict the observed values of the variables for
which vectors are being fitted.

The arrow heads are the normalised coefficients for scores1 and scores2,
and hence represent the normalised change in response for a unit change
in the scores1 and scores2 (the axis or site scores). As these are
normalised, the large the coefficient (change in response for unit
change in the site scores) the stringer the relationship between the
sites scores and the vector.

A key issue in the implementation is to consider the ordination space
into which you project vectors as a 2D configuration of points and we
want to relate these "locations" to the values of a secondary set of
variable.

HTH

G

> 
> thanks a lot for any good ideas..
> 
> gabriel
> 
> 
-- 
%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%
 Dr. Gavin Simpson             [t] +44 (0)20 7679 0522
 ECRC, UCL Geography,          [f] +44 (0)20 7679 0565
 Pearson Building,             [e] gavin.simpsonATNOSPAMucl.ac.uk
 Gower Street, London          [w] http://www.ucl.ac.uk/~ucfagls/
 UK. WC1E 6BT.                 [w] http://www.freshwaters.org.uk
%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%