gam.method               package:mgcv               R Documentation

_S_e_t_t_i_n_g _G_A_M _f_i_t_t_i_n_g _m_e_t_h_o_d

_D_e_s_c_r_i_p_t_i_o_n:

     This is a function of package 'mgcv' which allows  selection of
     the numerical method used to optimize the  smoothing parameter 
     estimation criterion for a gam.

     It is used to set argument 'method' of 'gam'.

_U_s_a_g_e:

     gam.method(am="magic",gam="outer",outer="nlm",pearson=FALSE,family=NULL)

_A_r_g_u_m_e_n_t_s:

      am: Which method to use for a pure additive model (i.e. identity
          link, gaussian errors). Either '"magic"' if the Wood (2004)
          method ('magic') is to be used, or '"mgcv"' if the faster,
          but less stable and general Wood (2000) method ('mgcv')
          should be used.

     gam: Which method to use in the generalized case (i.e. all case
          other than gaussian with identity link). '"perf.magic"' for
          the performance iteration (see details) with 'magic' as the
          basic estimation engine. '"perf.mgcv"' for performance
          iteration with 'mgcv' as the underlying estimation engine.
          '"perf.outer"' for 'magic' based performance iteration
          followed by outer iteration (see details). '"outer"' for pure
          outer iteration.

   outer: The optimization approach to use for outer iteration. '"nlm"'
          to use 'nlm' with exact first derivatives to optimize the
          smoothness selection criterion. '"nlm.fd"' to use 'nlm' with
          finite differenced first dericatives (slower and less
          reliable). '"optim"' to use the '"L-BFGS-B"' quasi-Newton
          method option of routine 'optim', with exact first
          derivatives.

 pearson: When using any sort of outer iteration, there is a choise
          between using GCV/UBRE scores based on the Pearson statistic,
          or based on the deviance. The Pearson versions result in
          smoother models, but this is often oversmoothing,
          particularly for `low count' data and binary regression.

  family: The routine is called by 'gam' to check the supplied method
          argument. In this circumstance the family argument is passed,
          to check that it works with the specified method. Negative
          binomial families only work  with performance iteration, and
          the method is reset to this if necessary.

_D_e_t_a_i_l_s:

     The performance iteration was suggested by Gu (and is rather
     similar to the PQL method in generalized linear mixed modelling).
     At each step of the P-IRLS (penalized iteratively reweighted least
     squares) iteration,  by which a gam is fitted, the smoothing
     parameters are estimated by GCV or UBRE applied to the working
     penalized linear modelling problem. In most cases, this process
     converges and gives smoothness estimates that perform well. It is
     usually very fast, since smoothing parameters are estimated
     alongside other model coefficients in a single P-IRLS process.

     The performance iteration has two disadvantages. (i) in the
     presence of co-linearity or concurvity (a frequent problem when
     spatial smoothers are included in a model with other covariates)
     then the process can fail to converge. Suppose we start with some
     coefficient and smoothing parameter estimates, implying a working
     penalized linear model: the optimal smoothing parameters and
     coefficients for this working model may in turn imply a working 
     model for which the original estimates are better than the most
     recent estimates. This sort of effect can prevent convergence.

     Secondly it is often possible to find a set of smoothing
     parameters that result in a lower GCV or UBRE score, for the final
     working model, than the final score that results from the
     performance iterations. This is because the performance iteration
     is only approximately optimizing this score (since optimization is
     only performed on the working model). The disadvantage here is not
     that the model with lower score would perform better (it usually
     doesn't), but rather that it makes model comparison on the basis
     of GCV/UBRE score rather difficult. 

     Both disadvantages of performance iteration are surmountable by
     using what is basically O'Sullivan's (1986) suggestion. Here the
     P-IRLS scheme is iterated to convergence for a fixed set of
     smoothing parameters, with an appropriate GCV/UBRE score evaluated
     at convergence. This score at convergence is optimized in some
     way. This is termed '"outer"' optimization, since the optimization
     is outer to the P-IRLS loop. Outer iteration is slower than
     performance iteration.

     The `appropriate GCV/UBRE' score in the previous paragraph can be
     defined in one of two ways either (i) the deviance, or (ii) the
     Pearson statistic can be used in place of the residual sum of
     squares in the GCV/UBRE score. (ii) makes the GCV/UBRE score
     correspond to the score for the working linear model at
     convergence of the P-IRLS, but in practice tends to result in
     oversmoothing,  particularly with low n binomial data, or low mean
     counts. Hence the default is to use (i).

     Several alternative optimisation methods can be used for outer
     optimization. 'nlm' can be used with finite differenced first
     derivatives. This is not ideal theoretically, since it is possible
     for the finite difference estimates of derivatives to be very
     badly in error on rare occasions when the P-IRLS convergence
     tolerance is close to being matched exactly, so that two
     components of a finite differenced derivative require different
     numbers of iterations of P-IRLS in their evaluation. An
     alternative is provided in which 'nlm' uses numerically exact
     first derivatives, this is faster and less problematic than the
     other scheme. Finally, a quasi-Newton scheme with exact derivtives
     can be used instead, based on 'optim'. In practice this usually
     seems to be slower than the 'nlm' method.  

     It is possible to iterate the performance iteration to convergence
     and then improve the smoothing parameter estimates using outer
     iteration: only a few steps are usually required in the outer
     iteration in this case, so it may be quite efficient, but it is
     not recommended if the performance iteration itself is
     non-convergent. When using `pure' outer iteration, a single step
     of the performance iteration is in fact taken first, to obtain
     estimates of the scale of the GCV/UBRE objective: starting values
     for the smoothing parameters are obtained using 'initial.sp'.

     In summary: performance iteration is fast, but can fail to
     converge. Outer iteration is slower, but more reliable. At present
     only performance iteration is available for negative binomial
     families.

_A_u_t_h_o_r(_s):

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

_R_e_f_e_r_e_n_c_e_s:

     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/>

_S_e_e _A_l_s_o:

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

