madifa with qualitative variables

Hello Jeanne,

I feel that it is not possible to use qualitative variables with madifa i.e.
using a Hill and Smith analysis instead of a principal component analysis on
the environmental table. Indeed, I receive the following error : "Error in
eigen(W) : infinite or missing values in 'x'" whereas the same command line
is ok with enfa. In madifa help, it is only written that the first argument
must be a dudi object not a pca. Is a trick exist to use a dudi.hillsmith
result instead of a dudi.pca as first argument in madifa ?
   

Indeed, the MADIFA's properties have not been well explored in the case 
of nominal variables... in addition, the current algorithm implemented 
in the function madifa relies on the inversion of the matrix of "used 
covariances", which is not possible in the case where qualitative 
variables are in the data (the matrix is not inversible, explaining the 
error message).
An alternative algorithm to perform the MADIFA is described in

@ARTICLE{,
   author = {Calenge, C. and Basille, M.},
   title = {A general framework for the statistical exploration of the 
ecological niche},
   journal = {Journal of Theoretical Biology},
   year = {2008},
   volume = {252},
   pages = {674-685}
}

and is implemented in the function gnesfa (this method place the ENFA 
and the MADIFA in a more general framework).
Thus, the command:

madifa(toto, pr)

is exactly the same as:

gnesfa(toto, Reference=pr)

though the latter do not rely on matrix inversion.
This solves the technical problem of matrix inversion, but not the 
problem of the meaning of the results, which is an open issue...
HTH,
Best regards,


Cl?ment Calenge

Cl?ment CALENGE
Cellule d'appui ? l'analyse de donn?es
Direction des Etudes et de la Recherche
Office national de la chasse et de la faune sauvage
Saint Benoist - 78610 Auffargis
tel. (33) 01.30.46.54.14