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

[gabriel singer]

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.singer at univie.ac.at