concorgmreg              package:concor              R Documentation

_R_e_g_r_e_s_s_i_o_n _o_f _s_u_b_s_e_t_s _Y_j _b_y _s_u_b_s_e_t_s _X_i

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

     Regression of subsets Yj by subsets Xi for comparing all the
     explanatory-explained pairs (Xi,Yj). SUCCESSIVE SOLUTIONS

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

     concorgmreg(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 p_i=sum(px)=p. px is the
          partition vector of the columns of x.

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

       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{rho2}(cx_i[,1],y_j*v_j[,1]) mbox{var}(y_j*v_j[,1]) is the
     optimized criterion. The second solution is calculated from the
     same criterion, but with y_j-y_j*v_j[,1]*v_j[,1]' instead of the
     matrices yj and with orthogonalities for having two by two zero
     correlated the explanatory components defined for each matrix xi.
     And so on for the other solutions. One solution k associates kx
     explanatory components (in cx[,k]) to ky explained components.
     When kx =1 (px=p), take concoreg function

     This function uses the concorgm 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:

     Hanafi & Lafosse (2004) Regression of a multi-set by another based
     on an extension of the SVD. COMPSTAT'2004 Symposium

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

