bruto                  package:mda                  R Documentation

_F_i_t _a_n _A_d_d_i_t_i_v_e _S_p_l_i_n_e _M_o_d_e_l _b_y _A_d_a_p_t_i_v_e _B_a_c_k_f_i_t_t_i_n_g

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

     Fit an additive spline model by adaptive backfitting.

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

     bruto(x, y, w, wp, dfmax, cost, maxit.select, maxit.backfit, 
           thresh = 0.0001, trace.bruto = FALSE, start.linear = TRUE,
           fit.object, ...)

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

       x: a matrix of numeric predictors (does not include the column
          of 1s).

       y: a vector or matrix of responses.

       w: optional observation weight vector.

      wp: optional weight vector for each column of 'y'; the RSS and
          GCV criteria use a weighted sum of squared residuals.

   dfmax: a vector of maximum df (degrees of freedom) for each term.

    cost: cost per degree of freedom; default is 2.

maxit.select: maximum number of iterations during the selection stage.

maxit.backfit: maximum number of iterations for the final backfit stage
          (with fixed lambda).

  thresh: convergence threshold (default is 0.0001); iterations cease
          when the relative change in GCV is below this threshold.

trace.bruto: logical flag.  If 'TRUE' (default) a progress report is
          printed during the fitting.

start.linear: logical flag.  If 'TRUE' (default), the model starts with
          the linear fit.

fit.object: This the object returned by 'bruto()'; if supplied, the
          same model is fit to the presumeably new 'y'.

     ...: further arguments to be passed to or from methods.

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

     A multiresponse additive model fit object of class '"bruto"' is
     returned.  The model is fit by adaptive backfitting using
     smoothing splines.  If there are 'np' columns in 'y', then 'np'
     additive models are fit, but the same amount of smoothing (df) is 
     used for  each term.  The procedure chooses between 'df = 0' (term
     omitted), 'df = 1' (term linear) or 'df > 0' (term fitted by
     smoothing spline).  The model selection is based on an
     approximation to the  GCV criterion, which is used at each step of
     the backfitting procedure.  Once the selection process stops, the
     model is backfit using the chosen amount of smoothing.

     A bruto object has the following components of interest: 

  lambda: a vector of chosen smoothing parameters, one for each column
          of 'x'.

      df: the df chosen for each column of 'x'.

    type: a factor with levels '"excluded"', '"linear"' or '"smooth"',
          indicating the status of each column of 'x'.

gcv.select gcv.backfit df.select: The sequence of gcv values and df
          selected during the execution of the function.

     nit: the number of iterations used.

fitted.values: a matrix of fitted values.

residuals: a matrix of residuals.

    call: the call that produced this object.

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

     Trevor Hastie and Rob Tibshirani, _Generalized Additive Models_,
     Chapman and Hall, 1990 (page 262).

     Trevor Hastie, Rob Tibshirani and Andreas Buja ``Flexible
     Discriminant Analysis by Optimal Scoring'' AT&T Bell Laboratories
     Technical Memorandum, February 1993.

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

     'predict.bruto'

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

     data(trees)
     fit1 <- bruto(trees[,-3], trees[3])
     fit1$type
     fit1$df
     ## examine the fitted functions
     par(mfrow=c(1,2), pty="s")
     Xp <- matrix(sapply(trees[1:2], mean), nrow(trees), 2, byrow=TRUE)
     for(i in 1:2) {
       xr <- sapply(trees, range)
       Xp1 <- Xp; Xp1[,i] <- seq(xr[1,i], xr[2,i], len=nrow(trees))
       Xf <- predict(fit1, Xp1)
       plot(Xp1[ ,i], Xf, xlab=names(trees)[i], ylab="", type="l")
     }

