pls1c                  package:pls                  R Documentation

_U_n_i_v_a_r_i_a_t_e _P_a_r_t_i_a_l _L_e_a_s_t _S_q_u_a_r_e_s _R_e_g_r_e_s_s_i_o_n

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

     Performs univariate partial least squares (PLS) regression of a
     vector on a matrix of explanatory variables using a modified
     version of an algorithm given in Helland (1988)

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

     pls1c(X, y, K=min(dx[1]-1,dx[2]))

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

       X: Matrix of explanatory variables. Each column represents a
          variable and each row an observation. The columns of this
          matrix are assumed to have been  centred. The number of rows
          of `X' should equal the number of observations in `y'. `NA's
          and `Inf's are not allowed.  

       y: Vector of responses. `y' is assumed to have been centred.
          `NA's and `Inf's are not allowed. 

       K: Number of PLS factors to fit in the PLS regression. This must
          be less than or equal to the rank of `X'. 

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

     Univariate Partial Least Squares Regression is an example of a
     regularised regression method. It creates a lower dimensional
     representation of the original explanatory variables and uses this
     representation in an ordinary least squares regression of the
     response variables. (cf. Principal Components Regression). Unlike
     Principal Components Regression, PLS regression chooses the lower
     dimensional representation of the original explanatory variables
     with reference to the response variable `y'.

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

     a vector of regression coefficients

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

     Denham, M. C. (1992). Implementing partial least squares.
     Technical Report. Liverpool University

     Helland, I. S. (1988). On the Structure of partial least squares
     regression, Communications in Statistics, 17, pp. 581-607

     Martens, H.  and Naes, T. (1989). Multivariate Calibration. Wiley,
     New York.

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

     `pls1a', `pls1b', `svdpls1a', `svdpls1b',`svdpls1c'

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

     data(USArrests)
     attach(USArrests)
     pls1c(scale(cbind(Murder, Assault, UrbanPop),scale=FALSE), 
           scale(Rape,scale=FALSE), 2)

