| gam.control {mgcv} | R Documentation |
This is an internal function of package mgcv which allows control of the numerical options for fitting a GAM.
Typically users will want to modify the defaults if model fitting fails to converge, or if the warnings are generated which suggest a
loss of numerical stability during fitting.
gam.control(irls.reg=0.0,epsilon = 1e-04, maxit = 20,globit = 20,
mgcv.tol=1e-6,mgcv.half=15,nb.theta.mult=10000, trace = FALSE,
fit.method="magic",perf.iter=TRUE,rank.tol=.Machine$double.eps^0.5)
irls.reg |
For most models this should be 0. The iteratively re-weighted least squares method
by which GAMs are fitted can fail to converge in some circumstances. For example data with many zeroes can cause
problems in a model with a log link, because a mean of zero corresponds to an infinite range of linear predictor
values. Such convergence problems are caused by a fundamental lack of identifiability, but do not show up as
lack of identifiability in the penalized linear model problems that have to be solved at each stage of iteration.
In such circumstances it is possible to apply a ridge regression penalty to the model to impose identifiability, and
irls.reg is the size of the penalty. The penalty can only be used if fit.method=="magic".
|
epsilon |
This is used for judging conversion of the GLM IRLS loop in gam.fit. |
maxit |
Maximum number of IRLS iterations to perform using cautious GCV/UBRE optimization, after globit
IRLS iterations with normal GCV optimization have been performed. Note that fit method "magic" makes no distinction
between cautious and global optimization. |
globit |
Maximum number of IRLS iterations to perform with normal GCV/UBRE optimization. If convergence is not achieved after these
iterations then a further maxit iterations will be performed using cautious GCV/UBRE optimization. |
mgcv.tol |
The convergence tolerance parameter to use in GCV/UBRE optimization. |
mgcv.half |
If a step of the GCV/UBRE optimization method leads to a worse GCV/UBRE score, then the step length is halved. This is the number of halvings to try before giving up. |
nb.theta.mult |
Controls the limits on theta when negative binomial parameter is to be estimated. Maximum theta is set to
the initial value multiplied by nb.theta.mult, while the minimum value is set to the initial value divided by
nb.theta.mult. |
trace |
Set this to TRUE to turn on diagnostic output. |
fit.method |
set to "mgcv" to use the method described in Wood (2000). Set to "magic" to use a
newer numerically more stable method, which allows regularization and mixtures of fixed and estimated smoothing parameters.
Set to "fastest" to use "mgcv" for single penalty models and "magic" otherwise. |
perf.iter |
set to TRUE to use Gu's approach to finding smoothing
parameters in which GCV or UBRE is
applied to the penalized linear modelling problem produced at each IRLS iteration. This method is very fast, but means that it
is often possible to find smoothing parameters yielding a slightly lower GCV/UBRE score by perturbing some of the estimated
smoothing parameters a little. Technically this occurs because the performance iteration effectively neglects the dependence of the
iterative weights on the smoothing parameters. Setting perf.iter to FALSE uses O'Sullivan's approach in which
the IRLS is run to convergence for each trial set of smoothing parameters. This is much slower, since it uses nlm with
finite differences and requires many more IRLS steps. |
rank.tol |
The tolerance used to estimate rank when using fit.method="magic". |
With fit method "mgcv",
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 is not achieved within globit iterations, 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.
Simon N. Wood simon@stats.gla.ac.uk
Gu and Wahba (1991) Minimizing GCV/GML scores with multiple smoothing parameters via the Newton method. SIAM J. Sci. Statist. Comput. 12:383-398
Wood, S.N. (2000) Modelling and Smoothing Parameter Estimation with Multiple Quadratic Penalties. J.R.Statist.Soc.B 62(2):413-428
Wood, S.N. (2003) Thin plate regression splines. J.R.Statist.Soc.B 65(1):95-114
http://www.stats.gla.ac.uk/~simon/