Re: [R] Correspondence and detrended correspondence analysis

From: Gavin Simpson <>
Date: Sat, 19 Apr 2008 11:18:25 +0100

On Fri, 2008-04-18 at 18:45 +0000, Monica Pisica wrote:
> Hi,
> I hope someone knows the answer to this or has a real good reference
> about it (I am using Legendre & Legendre, Numerical Ecology, 1998)....
> My data is a data.frame with locations as rows and vegetation
> assemblages / species as columns. I've done a PCA, a correspondance
> analysis (CA) using ca in ca package and a detrended correspondance
> analysis (DCA) using decorana from vegan package. As far as i
> understand what i've done .... the relationships between vegetation
> categories and locations should be similar in all 3 analysis, although
> the 'arch' in locations / sites seen in the CA plot should be flatten
> out by the DCA - which it is!.
> My problem is that the locations / sites are flipped in the DCA plot
> versus PCA or CA plots (locations with positive coordinates now have
> negative coordinates in DCA versus CA or PCA), although the vegetation
> categories keep same relationships between them in all three plots -
> which is expected. If some code is required i can provide it but i
> didn't want to clutter the message too much. But i am providing the
> resulting plots in case they will make my problem clearer.

The sign of the eigenvectors (axis scores) is not defined, just the magnitude; using the same software on different machines may produce "flipped". Furthermore, the same analysis, PCA say, done using different software but on the same machine may not have the same sign, i.e. be flipped, depending on algorithm used etc.

There is nothing wrong here. You'd be better off asking yourself which is the appropriate technique to fit for your data rather than fitting them all...


> PCA plot:
> CA plot:
> DCA plot:
> DCA how i would expect it:
> Any thoughts on this will be very much appreciated,
> Monica
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 Dr. Gavin Simpson             [t] +44 (0)20 7679 0522
 ECRC, UCL Geography,          [f] +44 (0)20 7679 0565
 Pearson Building,             [e]
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