assist (version 2.0)

gdmudr: Interface of dbmdr, dbimdr, dgmdr, dpmdr in GRKPACK.

Description

To calculate a spline estimate with multiple smoothing parameters for non-Gaussian data

Usage

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)

Arguments

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 i

vmu

a character string specifying a method for choosing the smoothing parameter. "v", "m" and "u" represent GCV, GML and UBR respectively. "u$\sim$", 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.

Value

• 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 $log10(theta)$.
• nlaht{ the estimate of $log10(nobs*lambda)$. }
• 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.

References

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.

See Also

dsidr, dmudr, gdsidr, ssr