corresp                 package:MASS                 R Documentation

_S_i_m_p_l_e _C_o_r_r_e_s_p_o_n_d_e_n_c_e _A_n_a_l_y_s_i_s

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

     Find the principal canonical correlation and corresponding row-
     and column-scores from a correspondence analysis of a two-way
     contingency table.

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

     corresp(x, nf=1, ...)

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

       x: The function is generic, accepting various forms of the
          principal argument for specifying a two-way frequency table. 
          Currently accepted forms are matrices, data frames (coerced
          to frequency tables), objects of class `"crosstabs"' and
          formulae of the form `~ F1 + F2', where `F1' and `F2' are
          factors. 

      nf: The number of factors to be computed. Note that although 1 is
          the most usual, one school of thought takes the first two
          singular vectors for a sort of biplot. 

     ...: If the principal argument is a formula, a data frame may be
          specified as well from which variables in the formula are
          preferentially satisfied. 

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

     See the reference.  The `plot' method produces a graphical
     representation of the table if `nf=1', with the areas of circles
     representing the numbers of points.  If `nf' is two or more the
     `biplot' method is called, which plots the second and third
     columns of the matrices `A = Dr^(-1/2) U L' and `B = Dc^(-1/2) U
     V' where the singular value decomposition is `U L V'.  Thus the
     x-axis is the canonical correlation times the row and column
     scores. Although this is called a biplot, it does not have any
     useful inner product relationship between the row and column
     scores.  Think of this as an equally-scaled plot with two
     unrelated sets of labels.

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

     An list object of class `"correspondence"' for which `print',
     `plot' and `biplot' methods are supplied.  The main components are
     the canonical correlation(s) and the row and column scores.

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

     Venables & Ripley (1999), chapter 11.

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

     `svd', `princomp'

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

     data(quine)
     ct <- corresp(~ Age + Eth, data=quine)
     ct
     plot(ct)

     data(caith)
     library(mva)
     corresp(caith)
     biplot(corresp(caith, nf=2))

