lm.ridge                package:MASS                R Documentation

_R_i_d_g_e _R_e_g_r_e_s_s_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Fit a linear model by ridge regression.

_U_s_a_g_e:

     lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,
              x = FALSE, y = FALSE, contrasts = NULL, ...)

_A_r_g_u_m_e_n_t_s:

 formula: a formula expression as for regression models, of the form
          'response ~ predictors'. See the documentation of 'formula'
          for other details. 

    data: an optional data frame in which to interpret the variables
          occurring in 'formula'. 

  subset: expression saying which subset of the rows of the data should
           be used in the fit.  All observations are included by
          default. 

na.action: a function to filter missing data. 

  lambda: A scalar or vector of ridge constants. 

   model: should the model frame be returned? 

       x: should the design matrix be returned? 

       y: should the response be returned? 

contrasts: a list of contrasts to be used for some or all of 

     ...: additional arguments to 'lm.fit'. 

_V_a_l_u_e:

     A list with components

    coef: matrix of coefficients, one row for each value of 'lambda'. 

  scales: scalings used on the X matrix. 

   Inter: was intercept included? 

  lambda: vector of lambda values 

      ym: mean of 'y' 

      xm: column means of 'x' matrix 

     GCV: vector of GCV values 

    kHKB: HKB estimate of the ridge constant. 

     kLW: L-W estimate of the ridge constant. 

_R_e_f_e_r_e_n_c_e_s:

     Brown, P. J. (1994) _Measurement, Regression and Calibration_
     Oxford.

_S_e_e _A_l_s_o:

     'lm'

_E_x_a_m_p_l_e_s:

     data(longley)
     names(longley)[1] <- "y"
     lm.ridge(y ~ ., longley)
     plot(lm.ridge(y ~ ., longley,
                   lambda = seq(0,0.1,0.001)))
     select(lm.ridge(y ~ ., longley,
                    lambda = seq(0,0.1,0.0001)))
     # modified HKB estimator is 0.0042754
     # modified L-W estimator is 0.032295
     # smallest value of GCV  at 0.0028

