

svdpls1b(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) regres-
     sion of a vector on a matrix of explanatory variables
     using the Orthogonal Loadings Algorithm.

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

     svdpls1b(X, y, K=r)

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

       X: Matrix of explanatory variables. Each column rep-
          resents 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 regres-
          sion. 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 exam-
     ple 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. (1994).  Implementing partial least
     squares.  Statistics and Computing (to appear)

     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 Cali-
     bration.  Wiley, New York.

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

     pls1a,pls1b,pls1c,svdpls1a,svdpls1c

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

     data(crimes)
     attach(crimes)
     svdpls1b(scale(cbind(Murder, Assault, UrbanPop),scale=FALSE),
           scale(Rape,scale=FALSE), 2)

