This routine estimates a GAM (any quadratically penalized GLM) given log smoothing paramaters, and evaluates derivatives of the smoothness selection scores of the model with respect to the log smoothing parameters. Calculation of exact derivatives is generally faster than approximating them by finite differencing, as well as generally improving the reliability of GCV/UBRE/AIC/REML score minimization.
The approach is to run the P-IRLS to convergence, and only then to iterate for first and second derivatives.
Not normally called directly, but rather service routines for gam.
gam.fit3(x, y, sp, Eb ,UrS=list(),
weights = rep(1, nobs), start = NULL, etastart = NULL,
mustart = NULL, offset = rep(0, nobs), U1 = diag(ncol(x)),
Mp = -1, family = gaussian(), control = gam.control(),
intercept = TRUE,deriv=2,gamma=1,scale=1,
printWarn=TRUE,scoreType="REML",null.coef=rep(0,ncol(x)),
pearson.extra=0,dev.extra=0,n.true=-1,...)gaussian()glm.controlTRUE or
FALSEFALSE to suppress some warnings. Useful in
order to ensure that some warnings are only printed if they apply to the final
fitted model, rather than an intermediate used in optimization.glm.fit with some
modifications to allow (i) for quadratic penalties on the log likelihood;
(ii) derivatives of the model coefficients with respect to
log smoothing parameters to be obtained by use of the implicit function theorem and
(iii) derivatives of the GAM GCV, UBRE/AIC, REML or ML scores to be
evaluated at convergence. In addition the routines apply step halving to any step that increases the penalized deviance substantially.
The most costly parts of the calculations are performed by calls to compiled C code (which in turn calls LAPACK routines) in place of the compiled code that would usually perform least squares estimation on the working model in the IRLS iteration.
Estimation of smoothing parameters by optimizing GCV scores obtained at convergence of the P-IRLS iteration was proposed by O'Sullivan et al. (1986), and is here termed `outer' iteration.
Note that use of non-standard families with this routine requires modification
of the families as described in fix.family.link.
Wood, S.N. (2008) Fast stable direct fitting and smoothness selection for generalized additive models. J.R.Statist. Soc. B 70(3):495-518
gam.fit, gam, mgcv, magic