scam (version 1.0)

scam.fit: Newton-Raphson method to fit SCAM

Description

This routine estimates SCAM coefficients given log smoothing parameters using the Newton-Raphson method. The estimation of the smoothing parameters by the GCV/UBRE score optimization is outer to the model fitting. Routine gcv.ubre_grad evaluates the first derivatives of the smoothness selection scores with respect to the log smoothing parameters. Routine bfgs_gcv.ubre estimates the smoothing parameters using the BFGS method. The function is not normally called directly, but rather service routines for scam.

Usage

scam.fit(G,sp, SVD=TRUE,ee,eb,esp, maxit=200,epsilon=1e-8,start=NULL,    
          etastart=NULL, mustart=NULL)

Arguments

G

A list of items needed to fit a SCAM.

sp

The vector of smoothing parameters.

SVD

Logical, if TRUE (default) then svd is applied to the augmented working model matrix, otherwise the qr decomposition will be used (not recommended).

ee

Get the enviroment for the model coefficients.

eb

Get the enviroment for the model coefficients derivatives.

esp

Get the enviroment for the smoothing parameter.

maxit

Maximum iterations in the Newton-Raphson procedure.

epsilon

A positive scalar giving the tolerance at which the scaled distance between two successive penalized deviances is considered close enough to zero to terminate the algorithm.

start

Initial values for the model coefficients

etastart

Initial values for the linear predictor

mustart

Initial values for the expected values

Details

The routine applies step halving to any step that increases the penalized deviance substantially.

References

Pya, N. (2010) Additive models with shape constraints. PhD thesis. University of Bath. Department of Mathematical Sciences Wood, S.N. (2008) Fast stable direct fitting and smoothness selection for generalized additive models. J.R.Statist. Soc. B 70(3):495-518 Wood, S.N. (2009) Fast stable REML estimation of semiparametric GLMs. (to be published)

See Also

scam