concorsreg              package:concor              R Documentation

"_s_i_m_u_l_t_a_n_e_o_u_s _c_o_n_c_o_r_g_m_r_e_g"

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

     concorgmreg with the set of r solutions simultaneously optimized

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

     concorsreg(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:

     This function uses the concors function

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

     list with following components 

      cx: is a n.kx x r matrix of kx row blocks cxi (n x r). Each row
          block contains r partial explanatory components

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

  varexp: is a kx x ky x r array; for a fixed solution k, the matrix
          varexp[,,k] contains kxky explained variances obtained by a
          simultaneous regression of all the yj by all the xi, so the
          values mbox{rho2}(cx[n*(i-1)+1:n*i,k],y_j*v_j[,k])
          var(y_j*v_j[,k])

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

     See svdbips

_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)
     crs<-concorsreg(x,c(2,3),y,c(3,2,4),2)
     diag(t(crs$cx[1:10,])%*%y[,1:3]%*%crs$v[1:3,]/10)^2
     crs$varexp[1,1,]

