FCAk {PTAk} | R Documentation |
Performs a particular PTAk
data as a ratio Observed/Expected
under complete independence with metrics as margins of the multiple
contingency table (in frequencies).
FCAk(X,nbPT=3,nbPT2=1,minpct=0.01, smoothing=FALSE,smoo=rep(list( function(u)ksmooth(1:length(u),u,kernel="normal", bandwidth=3,x.points=(1:length(u)))$y),length(dim(X))), verbose=getOption("verbose"),file=NULL, modesnam=NULL,addedcomment="",chi2=TRUE,E=NULL)
X |
a multiple contingency table (array) of order k |
nbPT |
a number or a vector of dimension (k-2) |
nbPT2 |
if 0 no 2-modes solutions will be computed, 1 =all, >1 otherwise |
minpct |
numerical 0-100 to control of computation of future solutions at this level and below |
smoothing |
see SVDgen |
smoo |
see SVDgen |
verbose |
control printing |
file |
output printed at the prompt if NULL , or printed in the given ‘file’ |
modesnam |
character vector of the names of the modes, if NULL "mo 1 "
..."mo k " |
addedcomment |
character string printed if printt after the title of the analysis |
chi2 |
print the chi2 information when computing margins in FCAmet |
E |
if not NULL is an array with the same dimensions as X |
Gives the SVD-kmodes decomposition of the 1+chi^2/N of
the multiple contingency table of full count N=sum X <- {ijk...},
i.e. complete independence + lack of independence (including marginal
independences) as shown for example in Lancaster(1951)(see reference
in Leibovici(2000)). Noting P=X/N, a PTAk
of the
(k+1)-uple is done, e.g. for a three way contingency table
k=3 the 4-uple data and metrics is:
((D_I^{-1} otimes D_J^{-1} otimes D_K^{-1})P, quad D_I, quad D_J, quad D_K)
where the metrics are diagonals of the corresponding margins. For
full description of arguments see PTAk
. If E
is not NULL
an FCAk-modes relatively to a model is
done (see Escoufier(1985) and therin reference
Escofier(1984) for a 2-way derivation, e.g. for a three way contingency table
k=3 the 4-tuple data and metrics is:
((D_I^{-1} otimes D_J^{-1} otimes D_K^{-1})(P-E), quad D_I, quad D_J, quad D_K)
If E
was the complete independence (product of the margins)
then this would give an AFCk
but without looking at the
marginal dependencies (i.e. for a three way table no two-ways lack of
independence are looked for).
a FCAk
(inherits PTAk
) object
Didier Leibovici c3s2i@free.fr
Escoufier Y (1985) L'Analyse des correspondances : ses propriétés et ses extensions. ISI 45th session Amsterdam.
Leibovici D (1993) Facteurs à Mesures Répétées et Analyses Factorielles : applications à un suivi épidémiologique. Université de Montpellier II PhD Thesis in Mathématiques et Applications (Biostatistiques).
Leibovici D (2000) Multiway Multidimensional Analysis for Pharmaco-EEG Studies. (submitted) http://c3s2i.free.fr/cv/recentpub.html
# try the demo # demo.FCAk()