CORRESPONDENCE ANALYSIS (CA)

                                            What is it?

*       CA (= reciprocal averaging of Hill, 1973) is a `form' of PCA which uses a different
association coefficient (X^2);



*       Like PCA, eigenvector ordination method to reduce the dimensionality of a multivariate data
set;



*       Unlike PCA however data can be qualitative, semi-quantitative and quantitative data = VERY
useful in microfacies analysis;



*       Data need to be dimensionally homogeneous (same units) and > or = 0 !





                                     Microfacies versus Relays:

*       Sedimentary environments can be relatively well partitioned (1) or on the contrary grade
progressively into each other (2).



*       In the first case a microfacies (cluster analysis) approach is appropriate, in the second it
will be rather artificial and a crude representation of the reality.











































                                            In PAST 1.33

*      The PCA routine finds the eigenvalues and eigenvectors of the matrix containing the X2
distances between all data points:



  -     Scatter plot of samples (rows) in the CA coordinate system (main factor axes 1-3);

  -     Variables can be plotted also in the same coordinate system;

  -     A `Relay plot' is also available with CA first PC as the vertical axis and the original data
  point value (abundances) on the horizontal axis (samples in rows, variables in columns). It shows
  the variables ordered along a potential gradient;

  -     Detrended CA is also performed by PAST in two steps: straightening and spreading.



                                            Final words

*       CA is very powerful and largelly under-used in sedimentology and palaeoecology;



*       Ordination (PCA-CA) can (should?) be combined with cluster analysis, not especially
antagonistic:

    

            - Cluster analysis looks at pairwise distances among samples =    fine relationships,

           

            - Ordination (CA, PCA) considers the variability of the whole          association
matrix and thus brings out general gradients;



*       Methods exist to superimpose the two approaches;



*       Problem of extreme values in CA because of the X2. Very sensitive to rare species/components
which tend to be located at the extremes in the ordination plot.

                                             References

*      PAST: http://folk.uio.no/ohammer/past/



*      AnalLog: contact A. Lees at alanlees@gofree.indigo.ie



*      (very) Good websites:



      - http://ordination.okstate.edu/

      - http://www.plantbio.ohiou.edu/epb/instruct/multivariate/multivariate.htm

      - http://www.okstate.edu/artsci/botany/ordinate/software.htm#method

      - http://149.170.199.144/multivar/intro.htm



The bible...:

     Legendre, P. & Legendre, L. 1998. Numerical Ecology. Elsevier.