These routines estimates a GAM given log smoothing paramaters, and evaluate derivatives of the GCV and UBRE 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 score minimization.
gam.fit2 evaluates first derivatives, by accumulating them as P-IRLS
progresses. gam.fit3 uses a more efficient approach in which the P-IRLS
is first run to convergence, and only then are the derivatives evaluated by a
separate iteration. gam.fit3 can evaluate second as well as first derivatives.
Not normally called directly, but rather service routines for gam.
gam.fit2(x, y, sp, S=list(),rS=list(),off, H=NULL,
weights = rep(1, nobs), start = NULL, etastart = NULL,
mustart = NULL, offset = rep(0, nobs), family = gaussian(),
control = gam.control(), intercept = TRUE,deriv=TRUE,
gamma=1,scale=1,pearson=FALSE,printWarn=TRUE,...)
gam.fit3(x, y, sp, S=list(),rS=list(),off, H=NULL,
weights = rep(1, nobs), start = NULL, etastart = NULL,
mustart = NULL, offset = rep(0, nobs), family = gaussian(),
control = gam.control(), intercept = TRUE,deriv=2,use.svd=TRUE,
gamma=1,scale=1,printWarn=TRUE,...)off[i] indicates which parameter is the first one penalized
by S[[i]].off[i] indicates which parameter S[[i]][1,1] relates to.gaussian()glm.controlTRUE or
FALSETRUE or FALSE for gam.fit2, but 0, 1 or 2,
indicating the maximum order of differentiation to apply, for
gam.fit3TRUE) or the cheaper QR
(FALSE) as the second matrix decomposition of the final
derivative/coefficient evaluation method? Only used by gam.fit3.gam.fit2.FALSE 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 updating alongside the P-IRLS
iteration) and (iii) derivatives of the GAM GCV and UBRE scores to be
evaluated at convergence. In addition the routine applies step halving to any step that increases the penalized deviance substantially.
The most costly parts of the calculation 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.
gam.fit, gam, mgcv, magic