gavin and jari,
thanks, all makes sense.... I have to state that remembering the
discussion we had some weeks ago about fitting underlying (or
environmental) variables to a MDS ordination, that using vectorfit for
this purpose indeed would make sense for me, too. As long as before
choosing the representation as a vector (which would indeed suggest
linear behaviour over ordination space), a linear or at least monotonic
behaviour of the metric variable over ordination space is checked (e.g.
given using ordisurf).... or different opinions?
cheers, g
Gavin Simpson wrote:
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. Gabriel Singer
Department of Freshwater Ecology - University of Vienna
and Wassercluster Lunz Biologische Station GmbH
+43-(0)664-1266747
gabriel.sin...@univie.ac.at
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