scam.fit: Newton-Raphson method to fit SCAM

In scam: Shape Constrained Additive Models

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, etastart=NULL, mustart=NULL, env=env, 
              null.coef=rep(0,ncol(G$X)), control=scam.control())

Arguments

G	A list of items needed to fit a SCAM.
sp	The vector of smoothing parameters.

etastart	Initial values for the linear predictor.
mustart	Initial values for the expected values.
env	Get the enviroment for the model coefficients, their derivatives and the smoothing parameter.
null.coef	coefficients for a null model, needed for an ability to check for immediate divergence.
control	A list of fit control parameters returned by scam.control. It includes: maxit, a positive scalar which gives the maximum number of iterations for Newton's method; devtol.fit, a scalar giving the tolerance at which the relative penalized deviance is considered to be close enougth to 0 to terminate the algorithm; steptol.fit, a scalar giving the tolerance at which the scaled distance between two successive iterates is considered close enough to zero to terminate the algorithm; trace turns on or off some de-bugging information; print.warn, when set to FALSE turns off printing warning messages for step halving under non-finite exponentiated coefficients, non-finite deviance and/or if mu or eta are out of bounds.

Details

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

Author(s)

Natalya Pya <[e-mail]>

References

Pya, N. and Wood, S.N. (2015) Shape constrained additive models. Statistics and Computing, 25(3), 543-559

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. Journal of the Royal Statistical Society (B) 70(3):495-518

Wood, S.N. (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1):3-36

See Also

scam

scam documentation built on April 14, 2023, 5:12 p.m.