[R] canonical correspondence analysis

Graham Smith myotis at cix.compulink.co.uk
Sat Feb 17 12:18:00 CET 2001

In-Reply-To: <Pine.GSO.4.31.0102170733280.13118-100000 at auk.stats>


As an ecologist, this is something I am also interested in. However, as 
I am more an ecologist than a statistician, I quote from the MVSP 

"Canonical Correspondence Analysis(CCA;   ter Braak, 1986,1987) is a 
multivariate direct gradient analysis method that has become widely 
used in ecology. As the name suggests, this method is derived from 
correspondence  analysis, but has been modified to allow environmental 
data to be incorporated into the analysis. It is calculated using 
reciprocal averaging form of correspondence analysis. However, at each 
cycle of the averaging process, a multiple regression is performed of 
the sample scores on the environmental variables. New site scores are 
calculated based on this regression, and then the process is repeated , 
continuing until the scores stabilise. The result  is that the axes of 
the final ordination, rather than simply reflecting dimensions of the 
greatest variability in the species data, are restricted to the linear 
combinations of the environmental variables and the species data. In 
this way these two sets of data are then directly related."

Ref 1: ter Braak, CJF (1986) Canonical correspondence analysis: A new 
eigenfactor technique for multivariate direct gradient analysis. 
Ecology, 67:1167-1179

Ref 2: ter Braak, CJF (1987) The analysis of vegetation-environment 
relationships by canonical correspondence analysis. Vegetatio, 64:69-77

More general references are:

Jongman, RHG., Ter Braak, CJF., and,  van Tongeren, OFR. (1995) Data 
analysis in community and landscape ecology. CUP.

Kent, M. & Coker, P. (1992) Vegetation description and analysis: A 
practical approach. Wiley.

As far as I am aware, only MVSP and Canoco carry out CCA.

I hope this is of some interest and it does raise the general point 
that programming literate  ecologists don't seem to have yet fully 
embraced S-Plus or R. Having only recently found S-Plus and R myself I 
had rather hoped that some of the common ecological statistical tools 
such as CCA, Twinspan and Decorana, plus the miscellaneous tools 
described in Krebs (1989) might have found there way into an R package.

Krebs, CJ (1989) Ecological Methodology, Harper & Row. Now as a 2nd 
edition 1995?)


Graham S

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