tpsreg                package:funfits                R Documentation

_T_h_i_n _p_l_a_t_e _s_p_l_i_n_e _r_e_g_r_e_s_s_i_o_n
~_f_u_n_c_t_i_o_n _t_o _d_o ???

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

     A thin plate spline is result of minimizing the residual sum of
     squares subject to the constraint that the function have a certain
     level of smoothness (or roughness penalty). Here smoothness is
     quantified by the integral of squared m^th order derivatives. For
     one dimension and m=2 the roughness penalty is the integrated
     square of the second derivative of the function. For two
     dimensions the roughness penalty is the integral of the square of
     Dxx(f) + 2Dxy(f) +Dyy(f) (where Duv denotes the second partial
     derivative with respect to u and v.) Besides controlling the order
     of the derivatives, the value of m also determines the base
     polynomial that will be fit to the data. The degree of this
     polynomial will be (m-1).

     The smoothing parameter controls the amount that the data is
     smoothed. In the usual form this is denoted by lambda, the
     Lagrange multiplier of the minimization problem. Although this is
     an awkward scale, lambda =0 corresponds to no smoothness
     constraints and the data is interpolated.  lambda=infinity
     corresponds to just fitting the polynomial base model by ordinary
     least squares.  GCVPACK and this function use a more convenient
     scale for the smoothing parameter which in terms of lambda is
     log10(n*lambda). Thus interpolation and smoothing correspond to
     the extremes -infinity and +infinity.  The preferred is the
     effective number of parameters associated with the fitted surface.
     This scale is a complicated but monotone transformation of the
     smoothing parameter and these values are reported in gcv.grid and
     the eff.df components.

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

     tpsreg(x, y, spar, m=2, clean=T)

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

       x: A matrix of independent variables that are the arguments 

       y: Vector of dependent variables 

    spar: Value of the smoothing parameter.  

       m: Order of spline surface.  

   clean: Remove temporary files from the fitting process.  

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

     A list of class tpsreg. This includes the predicted surface in
     fitted.value and the residuals in residual. The results of the
     grid search to minimize the Generalized Cross Validation function
     is returned in gcv.grid.

_S_i_d_e _E_f_f_e_c_t_s:

     The computations are done by writing the data and job parameters
     to temporary UNIX files and executing a stand alone FORTRAN
     program. This strategy is preferred due to the memory requirements
     and the complexity of the thin plate spline algorithms. The bulk
     of the computations are done by a set of subroutines for thin
     plate spline problems: GCVPACK.

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

     See Additive Models by Hastie and Tibshriani.

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

     predict.tpsreg, plot.tpsreg, summary.tpsreg

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

     Fitting a surface to ozone measurements. 
     tpsreg(ozone$x, ozone$y) -> hold
     plot(hold) # residual plots and a plot of the GCV function verses the 
                # effective number of parameters



