gam.control               package: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.  To change the default
     choise of fitting method, see 'gam.method'.

Usage:

     gam.control(irls.reg=0.0,epsilon = 1e-06, maxit = 100,globit = 20,
                 mgcv.tol=1e-7,mgcv.half=15,nb.theta.mult=10000, trace = FALSE,
                 rank.tol=.Machine$double.eps^0.5,absorb.cons=TRUE,
                 nlm=list(),optim=list(),newton=list(),
                 outerPIsteps=1) 

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 not be used if the underlying fitting method
          is 'mgcv' (not the default - see 'gam.method' for details). 

 epsilon: This is used for judging conversion of the GLM IRLS loop in
          'gam.fit', 'gam.fit2' or 'gam.fit3'.

   maxit: Maximum number of IRLS iterations to perform. When using
          performance iteration (not default) then these iterations re
          in addition to 'globit' initial iterations.  If fitting is
          based on 'mgcv' (not default, even for performance iteration)
          then GCV/UBRE  will be cautious for these iterations.

  globit: Maximum number of initial IRLS iterations to perform (with
          normal  GCV/UBRE optimization) when using performance
          iteration (only). If convergence is  not achieved after these
          iterations then a further 'maxit' iterations will be
          performed. Ignored for default outer iteration.

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.

rank.tol: The tolerance used to estimate the rank of the fitting
          problem, for methods which deal with rank deficient cases
          (basically all except those based on 'mgcv').

absorb.cons: If 'TRUE' then the GAM is set up using a parameterization
          which requires no further constraint. Usually this means that
          all the smooths are automatically centered (i.e. they sum to
          zero over the covariate values). If 'FALSE' then the ordinary
          parameterizations of the smooths are used, which require
          constraints to be imposed during fitting. Not all estimation
          methods can deal with the 'FALSE' case.

     nlm: list of control parameters to pass to 'nlm' if this is used
          for outer estimation of smoothing parameters (not default).
          See details.

   optim: list of control parameters to pass to 'optim' if this is used
          for outer estimation of smoothing parameters (not default).
          See details.

  newton: list of control parameters to pass to default Newton
          optimizer used for outer estimation of log smoothing
          parameters. See details.

outerPIsteps: The number of performance interation steps used to
          initialize outer iteration. Less than 1 means that only one
          performance iteration step is taken to get the function
          scale, but the corresponding smoothing parameter estimates
          are discarded. 

Details:

     When outer iteration is used for fitting then the control list
     'nlm' stores control arguments for calls to routine 'nlm'. The
     list has the following named elements: (i) 'ndigit' is the number
     of significant digits in the GCV/UBRE score - by default this is
     worked out from 'epsilon'; (ii) 'gradtol' is the tolerance used to
     judge convergence of the gradient of the GCV/UBRE score to zero -
     by default set to '100*epsilon'; (iii) 'stepmax' is the maximum
     allowable log smoothing parameter step - defaults to 2; (iv)
     'steptol' is the minimum allowable step length - defaults to 1e-4;
     (v) 'iterlim' is the maximum number of optimization steps allowed
     - defaults to 200; (vi) 'check.analyticals' indicates whether the
     built in exact derivative calculations should be checked
     numerically - defaults to 'FALSE'. Any of these which are not
     supplied and named in the list are set to their default values.

     Outer iteration using 'newton' is controlled by the list 'newton'
     with the following elements : 'conv.tol' (default 1e-6) is the
     relative convergence tolerance; 'maxNstep' is the maximum length
     allowed for an element of the Newton search direction (default 5);
     'maxSstep' is the maximum length allowed for an element of the
     steepest descent direction (only used if Newton fails - default
     2); 'maxHalf' is the maximum number of step halvings to permit
     before giving up (default 30);  'use.svd' determines whether to
     use an SVD step or QR step for the part of fitting that determines
     problem rank, etc. (defaults to 'FALSE').

     Outer iteration using 'optim' is controlled using list 'optim',
     which currently has one element: 'factr' which takes default value
     1e7.

     When fitting is been done by calls to routine 'mgcv' (not
     default),  '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.wood@r-project.org

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

     Wood, S.N. (2004) Stable and efficient multiple smoothing
     parameter estimation for generalized additive models. J. Amer.
     Statist. Ass.

     <URL: http://www.maths.bath.ac.uk/~sw283/>

See Also:

     'gam.method'   'gam', 'gam.fit', 'glm.control'

