

   AAddddiittiivvee nnoonnppaarraammeettrriicc rreeggrreessssiioonn

        addreg(x, y, lam, nback=20, tol=1e-05, start, cost=1)

   AArrgguummeennttss::

          x: Matrix of independent variables

          y: Vector of independent variables

        lam: Vector of length P with values of the smoothing
             parameters. If missing then the parameters are
             found by generalized cross-validation.

      nback: Maximum number of iterations for backfitting.

        tol: Tolerance value for judging convergence of back-
             fitting.

      start: Matrix of starting values for the function esti-
             mates

       cost: Cost for each degree of freedom in the GCV crite-
             rion.

   DDeessccrriippttiioonn::

        Estimates the univariate functions using backfitting.
        If lambda is omitted in the call then at each step the
        smoothing parameter is estimated by minimizing the GCV
        criterion: GCV(lambda)=(1/n)* RSS/(n- p*2 + cost*(sum(
        J_i))**2

        Here J_i = tr(A_i) -2 where  A_i is the smoothing
        matrix for variable i.

        If p=1 and cost =1 this is the usual GCV function. A
        cost > 1 has the effect of being more conservative in
        choosing estimates that deviate from a linear function.
        Note that the effective number of parameters in the
        total model can be approximated by sum( tr( A_i)).

   VVaalluuee::

        A list of class addreg. Components fitted.values and
        residuals contain the results of the fit. pre-
        dicted.comp is matrix whose columns contain the esti-
        mates for the individual functions. The component trace
        has the effective number of parameters associated with
        each smoother and lambda has the corresponding smooth-
        ing parameters. Convergence information is in the com-
        ponent converge.

   SSeeee AAllssoo::

        plot.addreg, gam, predict.addreg

   EExxaammpplleess::

        # Additive model fit to the minitriathon data. A prediction of
        # run times based on the swim and bike performance.
        # The smoothing parameters found by GCV with cost=2.
        cbind( minitri$swim, minitri$bike)-> x
        addreg( x,minitri$run,cost=2)-> out
        plot( out) # summary plots of fits
        list( c(10,25), c(35,55))-> grid.list
        predict.surface(out, grid.list)-> out.p
        persp( out.p) # perspective plot of fitted surface

