

prcomp {mva}                                 R Documentation

_P_r_i_n_c_i_p_a_l _C_o_m_p_o_n_e_n_t_s _A_n_a_l_y_s_i_s

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

     Performs a principal components analysis on the given
     data matrix and returns the results as an object of
     class `prcomp'.

_U_s_a_g_e_:

     prcomp(x, retx = TRUE, center = TRUE, scale. = FALSE, tol = NULL)

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

       x: a matrix (or data frame) which provides the data
          for the principal components analysis.

    retx: a logical value indicating whether the rotated
          variables should be returned.

  center: a logical value indicating whether the variables
          should be shifted to be zero centered. Alter-
          nately, a vector of length equal the number of
          columns of `x' can be supplied.  The value is
          passed to `scale'.

   scale: a logical value indicating whether the variables
          should be scaled to have unit variance before the
          analysis takes place. The default is `FALSE' for
          consistency with S, but in general scaling is
          advisable. Alternately, a vector of length equal
          the number of columns of `x' can be supplied.  The
          value is passed to `scale'.

     tol: a value indicating the magnitude below which com-
          ponents should be omitted. With the default null
          setting, no components are omitted.  Other set-
          tings for tol could be `tol = 0' or `tol =
          sqrt(.Machine$double.eps)'.

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

     The calculation is done by a singular-value decomposi-
     tion of the data matrix, not by using eigen on the
     covariance matrix.  This is generally the preferred
     method for numerical accuracy.  The `print' method for
     the these objects prints the results in a nice format
     and the `plot' method produces a scree plot.

_V_a_l_u_e_:

     `prcomp' returns an list with class `"prcomp"' contain-
     ing the following components:

    sdev: the standard deviation of the principal components
          (i.e., the eigenvalues of the cov matrix, though
          the calculation is actually done with the singular
          values of the data matrix).

rotation: the matrix of variable loadings (i.e., a matrix
          whose olumns contain the eigenvectors).  The func-
          tion `princomp' returns this in the element `load-
          ings'.

       x: if `retx' is true the value of the rotated data
          (the data multiplied by the `rotation' matrix) is
          returned.

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

     Mardia, K. V., J. T. Kent, J and M. Bibby (1979), Mul-
     tivariate Analysis, London: Academic Press.

     Venables, W. N. and B. D. Ripley (1997), Modern Applied
     Statistics with S-PLUS, Springer-Verlag.

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

     `princomp', `cor', `cov', `svd', `eigen'.

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

     ## the variances of the variables in the
     ## USArrests data vary by orders of magnitude
     data(USArrests)
     prcomp(USArrests)
     prcomp(USArrests, scale = TRUE)
     plot(prcomp(USArrests))
     summary(prcomp(USArrests))

