gdsidr                package:assist                R Documentation

_I_n_t_e_r_f_a_c_e _o_f _d_b_s_d_r, _d_b_i_s_d_r, _d_g_s_d_r, _d_p_s_d_r _i_n _G_R_K_P_A_C_K.

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

     To calculate a spline estimate with single smoothing parameter for
     non-Gaussian data.

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

     gdsidr(y, q, s, family, vmu="v", varht=NULL, limnla=c(-10, 3), 
     maxit=30, job=-1, tol1=0, tol2=0, prec=1e-06)

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

       y: a numerical vector representing the response, or a matrix of
          two columns for binomial data with the first column as the
          largest possible counts and the second column as the counts
          actually obsered. 

       q: a square matrix of the same order as the length of y, with
          elements equal to the reproducing kernel evaluated at the
          design points. 

       s: the design matrix of the null space H_0 of size
          (length-of-y,dim(H_0)), with elements equal to the bases of
          H_0 evaluated at design points. 

  family: a string specifying the family of distribution. Families 
          supported  are  "binary", "binomial", "poisson" and "gamma"
          for Bernoulli, binomial, poisson, and gamma distributions
          respectively. Canonical links are used except for Gamma
          family where a log link is used. 

     vmu: a character string specifying a method for choosing the
          smoothing  parameter.  "v", "m" and "u" represent GCV, GML
          and UBR respectively. "u~", only used for non-Gaussian
          family, specifies UBR with estimated variance. Default is
          "v". 

   varht: needed only when vmu="u", which gives the fixed variance in
          calculation of the UBR function. Default is 1.0. 

  limnla: a vector of length 2, specifying a search range for the  n
          times smoothing parameter on log10 scale. Default is (-10,
          3). 

   maxit: maximum number of iterations allowed for the iteration in
          GRKPACK. 

     job: an integer representing the optimization method used to find
          the smoothing parameter.  The  options are job=-1:
          golden-section search on (limnla(1), limnla(2));  job=0:
          golden-section search with interval specified automatically; 
          job >0: regular grid search on  [limnla(1), limnla(2)] with
          #(grids) = job + 1. Default is -1.  

    tol1: the tolerance for elements of w's. Default is 0.0 which sets
          to square of machine precision.  

    tol2: tolerance for truncation used in `dsidr'. Default is 0.0
          which sets to square of machine precision. 

    prec: precision requested for stopping the iteration. Default is
          1e-06. 

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

    info: an integer that provides error message. info=0 indicates
          normal termination, info=-1 indicates dimension error, 
          info=-2 indicates F_{2}^{T} Q F_{2} !>= 0, info=-3 indicates
          vmu is out of scope, info=-4 indicates the algorithm fails to
          converge at the maxiter steps, info=-5 indicates there are
          some w's equals to zero, and info>0 indicates the matrix S is
          rank deficient with info=rank(S)+1.  

     fit: estimate of the function at design points. 

       c: estimates of c. 

       d: estimates of d. 

    resi: vector of working residuals. 

   varht: estimate of dispersion parameter. 

   nlaht: the estimate of log10(nobs*lambda). 

  limnla: searching range for nlaht.  

   score: the minimum GCV/GML/UBR score at the estimated smoothing
          parameter. When job>0, it gives a vector of GCV/GML/UBR
          functions evaluated at regular grid points. 

      df: equavilent degree of freedom. 

    nobs: length-of-y, number of observations. 

   nnull: dim(H_0), number of bases. 

s,qraux,jpvt: QR decomposition of S=FR, as from Linpack `dqrdc'. 

       q: first dim(H_0) columns gives F^{T} Q F_{1}, and its
          bottom-right corner gives tridiagonalization of F_{2}^{T} Q
          F_{2}. 

_A_u_t_h_o_r(_s):

     Chunlei Ke chunlei_ke@pstat.ucsb.edu and Yuedong Wang
     yuedong@pstat.ucsb.edu

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

     Wahba, G. (1990). Spline Models for Observational Data. SIAM, Vol.
     59.

     Wang, Y. (1997). GRKPACK: Fitting Smoothing Spline ANOVA Models
     for Exponential Families. Communications in Statistics: Simulation
     and Computation, 24: 1037-1059.

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

     'dsidr', 'dmudr', 'gdmudr', 'ssr'

