gdmudr                package:assist                R Documentation

_I_n_t_e_r_f_a_c_e _o_f _d_b_m_d_r, _d_b_i_m_d_r, _d_g_m_d_r, _d_p_m_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 multiple smoothing parameters
     for non-Gaussian data

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

     gdmudr(y, q, s, family, vmu = "v", varht = NULL, 
         init = 0, theta = NULL, tol1 = 0, tol2 = 0, prec1 = 1e-06, 
         maxit1 = 30, prec2 = 1e-06, maxit2 = 30) 

_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 list, or an array, of square matrices of the same order as
          the length of y, which are the reproducing kernels 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 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. 

    init: an integer of 0 or 1 indicating if initial values are
          provided for theta. If init=1, initial values are provided
          using theta. Default is 0. 

   theta: If `init=1', theta includes intial values for smoothing
          parameters. Default is NULL. 

    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. 

   prec1: precision requested for the minimum score value, where
          precision is the weaker of the absolute and relative
          precisions. Default is 1e-06. 

  maxit1: maximum number of iterations allowed for DMUDR subroutine.
          Default is 30. 

   prec2: precision requested for stopping the iteration. Default is
          1e-06. 

  maxit2: maximum number of iterations allowed for the iteration in
          GRKPACK. Default is 30. 

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

    info: an integer that provides error message. info=-1 indicates
          dimension error,  info=-2 idicates F_{2}^{T} Q_{*}^{theta}
          F_{2} !>= 0, info=-3 indicates tuning parameters are out of
          scope, info=-4 indicates dmudr fails to converge within
          maxit1 steps, info=-5 indicates dmudr fails to find a
          reasonable descent direction, info=-6 indicates GRKPACK fails
          to converge within maxit2 steps, info=-7 indicates there are
          some w's equals to zero,  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. 

   theta: estimates of parameters log10(theta).  

   score: the minimum GCV/GML/UBR score at the estimated smoothing
          parameters.  

      df: equavilent degree of freedom. 

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

   nnull: dim(H_0), number of bases. 

      nq: length(rk), number of reproducing kernels. 

s,q,y,init,maxit2: changed from the inputs. 

_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', 'gdsidr', 'ssr'

