CAIV                 package:CoCoAn                 R Documentation

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

     Multivariate analysis. This function perform correspondence
     analysis or constrained correspondence analysis.  This latter is
     better known under the name of canonical correspondence analysis. 
     This analysis finds coefficients of variables to obtain a row
     score of unit variance. This row score is used to compute by
     weighted averaging a column score of maximized variance.

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

     CAIV(L, E=diag(1, dim(L)[1], dim(L)[1]), normE=TRUE)

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

       L: a (i,j) matrix of non-negative number 

       E: an (i,p) optional matrix of p external variables

   normE: `TRUE' to normalize variables in matrix `E', `FALSE'
          otherwise

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

     This function compute correspondence analysis (enter `L') or
     constrained correspondence analysis (enter `L' and `E').  The
     function return the coefficient (B) to compute a row score of unit
     variance (R) that maximize the between-column inertia (column
     score in F obtained by weighting averaging).  D contains the
     intra-set covariance (correlation if `normE=TRUE').  For
     correspondence analysis, `CAIV(t(L))' gives a column score of unit
     variance that maximize the between-rows inertia. Note that this
     function does not use convenient rescaling and so is a little bit
     different of ter Braak's CCA. (We use the algorithm of Chessel et
     al.)

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

     A list with components If it is a LIST, use 

      ev: a vector containing eigenvalues

       B: coefficients of variables of `E' (only in constrained
          analysis)

       D: covariance matrix between external variables and row scores
          (only in constrained analysis)

       R: row coordinates of unit variance

       F: column coordinates of variance `ev[i]' 

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

     Stephane DRAY dray@biomserv.univ-lyon1.fr

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

     ter Braak (1986): Canonical correspondence analysis: a new
     eigenvector technique for multivariate direct gradient analysis.
     Ecology 67(5), 1167-1179.

     Chessel, Lebreton and Yoccoz (1987): Proprits de l'analyse
     canonique des correspondances; une illustration en hydrobiologie.
     Revue de Statistique Applique 35(4) 55-72.

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

     `CAIV.plot'

