FCAk                  package:PTAk                  R Documentation

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_D_e_s_c_r_i_p_t_i_o_n:

     Performs a particular 'PTAk'  data as a ratio Observed/Expected
     under complete independence with metrics as margins of the
     multiple contingency table (in frequencies).

_U_s_a_g_e:

      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)

_A_r_g_u_m_e_n_t_s:

       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

_D_e_t_a_i_l_s:

     Gives the SVD-_k_modes 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).

_V_a_l_u_e:

     a 'FCAk' (inherits 'PTAk') object

_A_u_t_h_o_r(_s):

     Didier Leibovici c3s2i@free.fr

_R_e_f_e_r_e_n_c_e_s:

     Escoufier Y (1985) _L'Analyse des correspondances : ses proprits
     et ses extensions_. ISI 45th session Amsterdam.

     Leibovici D (1993) _Facteurs  Mesures Rptes et Analyses
     Factorielles : applications  un suivi pidmiologique_.
     Universit de Montpellier II PhD Thesis in Mathmatiques et
     Applications (Biostatistiques).

     Leibovici D (2000) _Multiway Multidimensional Analysis for
     Pharmaco-EEG Studies_. (submitted) <URL:
     http://c3s2i.free.fr/cv/recentpub.html>

_S_e_e _A_l_s_o:

     'PTAk', 'FCAmet', 'summary.FCAk'

_E_x_a_m_p_l_e_s:

      # try the demo
        # demo.FCAk()

