gam.convergence             package:mgcv             R Documentation

GAM convergence and performance issues

Description:

     When fitting GAMs there is a tradeoff between speed of fitting and
     probability of fit convergence. The default fitting options
     specified by 'gam.method' (as the default for argument 'method' of
     'gam'), always opt for certainty of convergence over speed of fit.
     In the additive modelling contexts this means using fitting
     routine 'magic' rather than the slightly faster routine 'mgcv'. In
     the Generalized Additive Model case it means using `outer'
     iteration in preference to `performance iteration': see
     'gam.outer' for details. 

     It is possible for the default `outer' iteration to fail when
     finding intial smoothing parameters using a few steps of outer
     iteration (if you get a convergence failure message from 'magic'
     when outer iterating, then this is what has happened): lower
     'outerPIsteps' in 'gam.control' to fix this. 

     There are two things that you can do to speed up GAM fitting. (i)
     Change the 'method' argument to 'gam' so that `performance
     iteration' is used in place of the default outer iteration. See
     the 'perf.magic' option under 'gam.method', for example. Usually
     performance iteration converges well and it can be quicker than
     the default outer iteration.  (ii) For large datasets it may be
     worth changing the smoothing basis to use 'bs="cr"' (see 's' for
     details) for 1-d smooths, and to use 'te' smooths in place of 's'
     smooths for smooths of more than one variable. This is because the
     default thin plate regression spline basis '"tp"' is costly to set
     up for large datasets (much over 1000 data, say). Alternatively
     see the last few examples for 'gam'. 

     If the GAM estimation process fails to converge when using
     performance iteration, then switch to outer iteration via the
     'method' argument of 'gam' (see 'gam.method'). If it still fails,
     try increasing the number of IRLS iterations (see 'gam.control')
     or perhaps experiment with the convergence tolerance. 

     If you still have problems, it's worth noting that a GAM is just a
     (penalized) GLM and the IRLS scheme used to estimate GLMs is not
     guaranteed to converge. Hence non convergence of a GAM may relate
     to a lack of stability in the basic IRLS scheme. Therefore it is
     worth trying to establish whether the IRLS iterations are capable
     of converging. To do this fit the problematic GAM with all smooth
     terms specified with 'fx=TRUE' so that the smoothing parameters
     are all fixed at zero. If this `largest' model can converge then,
     then the maintainer  would quite like to know about your problem!
     If it doesn't converge, then its likely that your model is just
     too flexible for the IRLS process itself. Having tried increasing
     'maxit' in 'gam.control', there are several other possibilities
     for stabilizing the iteration. It is possible to try (i) setting
     lower bounds on the smoothing parameters using the 'min.sp'
     argument of 'gam': this may or may not change the model being
     fitted; (ii) reducing the flexibility of the model by reducing the
     basis dimensions 'k' in the specification of 's' and 'te' model
     terms: this obviously changes the model being fitted somewhat;
     (iii) introduce a small regularization term into the fitting via
     the 'irls.reg' argument of 'gam.control': this option obviously
     changes the nature of the fit somewhat, since parameter estimates
     are pulled towards zero by doing this. 

     Usually, a major contributer to fitting difficulties is that the
     model is a very poor description of the data.

Author(s):

     Simon N. Wood simon.wood@r-project.org

