Instability of ordination results under changes in input data order: explanations and remedies

Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used t...

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Bibliographic Details
Published in:Journal of vegetation science 1997-06, Vol.8 (3), p.447-454
Main Authors: Oksanen, Jari, Minchin, Peter R.
Format: Article
Language:English
Subjects:
Algorithm
Algorithms
cluster analysis
Clustering
Computer software
correlation analysis
Correspondence analysis
Datasets
Detrended correspondence analysis
Eigenanalysis
Eigenvalues
Eigenvectors
equations
Fortran
Forum
Input data
mathematical models
Non-linear rescaling
Ordination
plant ecology
Polls
Software bugs
statistical analysis
theory
Tolerance
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Summary:Correspondence analysis (CA) and its Detrended form (DCA) produced by the program CANOCO are unstable under reordering of the species and sites in the input data matrix. In CA, the main cause of the instability is the use of insufficiently stringent convergence criteria in the power algorithm used to estimate the eigenvalues. The use of stricter criteria gives results that are acceptably stable. The divisive classification program TWINSPAN uses CA based on a similar algorithm, but with extremely lax convergence criteria, and is thus susceptible to extreme instability. We detected an order-dependent programming error in the non-linear rescaling procedure that forms part of DCA. When this bug is corrected, much of the instability in DCA disappears. The stability of DCA solutions is further enhanced by the use of strict convergence criteria. In our trials, much of the instability occurred in axes 3 and 4, but ine should not assume that published two-dimensional ordinations are sufficiently accurate. Data sets which have pairs of almost equal eigenvalues among the first three axes could suffer from marked instability in the first two dimensions. We recommend that a debugged, strict version of CANOCO be released. Meanwhile, users can check the stability of their CA and DCA ordinations using the software that we have made available on the World Wide Web (http:// www.helsinki.fi/~jhoksane/). An accurate program for CA, a debugged, strict version of DECORANA (for DCA) and a strict version of TWINSPAN are also available at our site.
ISSN:1100-9233
1654-1103
DOI:10.2307/3237336