mgcv. It is a modification
of the function glm.control. It enables the user to set defaults for convergence
tolerance and maximum number of iterations when using
gam. Argument mgcv.tol controls the tolerence used to judge
multiple smoothing parameter convergence (default 1e-6). mgcv.half is the
maximum number of times to halve the step length in an iterative update of the
smoothing parameters if the step is failing to decrease the GCV/UBRE
score (default 15). Setting trace to TRUE will cause various
diagnostics to be produced as fitting progresses, including plots of the GCV function
and current minimum, against model EDF. maxit and globit control the maximum
iterations of the IRLS algorithm, as follows: the algorithm will first execute up to
globit steps in which the GCV/UBRE algorithm performs a global search for the best overall
smoothing parameter at every iteration, if convergence has not occured by then, then a further
maxit steps are taken, in which the overall smoothing parameter estimate is taken as the
one locally minimising the GCV/UBRE score and resulting in the lowest EDF change. The difference
between the two phases is only significant if the GCV/UBRE function develops more than one minima.
The reason for this approach is that the GCV/UBRE score for the IRLS problem can develop "phantom"
minimima for some models: these are minima which are not present in the GCV/UBRE score of the IRLS
problem resulting from moving the parameters to the minimum! Such minima can lead to convergence
failures, which are usually fixed by the second phase. See glm.control for more information.
Wood (2000) Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties. JRSSB 62(2):413-428
gam gam.fit