concorgm               package:concor               R Documentation

_A_n_a_l_y_z_i_n_g _a _s_e_t _o_f _p_a_r_t_i_a_l _l_i_n_k_s _b_e_t_w_e_e_n _X_i _a_n_d _Y_j

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

     Analyzing a set of partial links between Xi and Yj, SUCCESSIVE
     SOLUTIONS

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

     concorgm(x,px,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

      px: is a row vector which contains the numbers pi, i=1,...,kx, of
          the kx subsets xi of x : sum(pi)=sum(px)=p. px is the
          partition vector of x

      py: is the partition vector of y with ky subsets yj, j=1,...,ky

       r: is the wanted number of successive solutions rmax <=
          min(min(px),min(py),n)

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

     For the first solution, sum_i sum_j
     mbox{cov2}(x_i*u_i[,1],y_j*v_j[,1]) is the optimized criterion.
     The second solution is calculated from the same criterion, but
     with x_i-x_i*u_i[,1]*u_i[,1]' and y_j-y_j*v_j[,1]*v_j[,1]' instead
     of the kx+ky matrices xi and yj. And so on for the other
     solutions.  When kx=1 (px=p), take concor.m

     This function uses the svdbip function.

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

     list with following components 

       u: is a p x r matrix of kx row blocks ui (pi x r), the
          orthonormed partial axes of xi; associated partial
          components: xi*ui

       v: is a q x r matrix of ky row blocks vj (qj x r), the
          orthonormed partial axes of yj; associated partial
          components: yj*vj

    cov2: is a kx x ky x r array; for r fixed to k, the matrix contains
          kxky  squared covariances
          mbox{cov2}(x_i*u_i[,k],y_j*v_j[,k])^2, the partial links
          between xi and yj measured with the solution k.

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

     Kissita, Cazes, Hanafi & Lafosse (2004) Deux methodes d'analyse
     factorielle du lien entre deux tableaux de variables
     partitionnes. Revue de Statistique Applique, Vol 52, n 3,
     73-92.

_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)
     cg<-concorgm(x,c(2,3),y,c(3,2,4),2)
     diag(t(x[,1:2]%*%cg$u[1:2,])%*%y[,1:3]%*%cg$v[1:3,]/10)^2
     cg$cov2[1,1,]

