gam.control {mgcv} | R Documentation

## Setting GAM fitting defaults

### Description

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.

### Usage

    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)

### Arguments

`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"`.

### Details

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.

### Author(s)

Simon N. Wood simon@stats.gla.ac.uk

### References

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/

### See Also

`gam`, `gam.fit`, `glm.control`

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