concorcano              package:concor              R Documentation

_C_a_n_o_n_i_c_a_l _a_n_a_l_y_s_i_s _o_f _s_e_v_e_r_a_l _s_e_t_s _w_i_t_h _a_n_o_t_h_e_r _s_e_t

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

     Relative proximities of several subsets of variables Yj with
     another set X. SUCCESSIVE SOLUTIONS

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

     concorcano(x,y,py,r)

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

       x: is a n x p matrix of p centered variables

       y: is a n x q matrix of q centered variables

      py: is a row vector which contains the numbers qi, i=1,...,ky, of
          the ky subsets yi of y : sum_i q_i=sum(py)=q. py is the
          partition vector of y

       r: is the wanted number of successive solutions

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

     The first solution calculates a standardized canonical component
     cx[,1] of x associated to ky standardized components cyi[,1] of yi
     by maximizing sum_i rho(cx[,1],cy_i[,1])^2.

     The second solution is obtained from the same criterion, with ky
     orthogonality constraints for having rho(cyi[,1],cyi[,2])=0 (that
     implies rho(cx[,1],cx[,2])=0).  For each of the 1+ky sets, the r
     canonical components are 2 by 2 zero correlated.

     The ky matrices (cx)'*cyi are triangular.

     This function uses concor function.

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

     list with following components 

      cx: is n x r matrix of the r canonical components of x

      cy: is n.ky x r matrix. The ky blocks cyi of the rows n*(i-1)+1 :
          n*i contain the r canonical components relative to Yi

    rho2: is a ky x r matrix; each column k contains ky squared
          canonical correlations rho(cx[,k],cy_i[,k])^2

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

     Hanafi & Lafosse (2001) Generalisation de la regression lineaire
     simple pour analyser la dependance de K ensembles de variables
     avec un K+1 eme.  Revue de Statistique Appliquee vol.49, n.1

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

     x<-matrix(runif(50),10,5);y<-matrix(runif(90),10,9)
     x<-scale(x);y<-scale(y)
     ca<-concorcano(x,y,c(3,2,4),2)
     diag(t(ca$cx)%*%ca$cy[1:10,]/10)^2
     ca$rho2[1,]

