mgcv-package              package:mgcv              R Documentation

GAMs with GCV smoothness estimation and GAMMs by REML/PQL

Description:

     'mgcv' provides functions for generalized additive modelling  and
     generalized additive mixed modelling (including variable
     coefficient models). Particular features of the package are
     facilities for automatic smoothness selection, and the provision
     of a variety of smooths of more than one variable. User defined
     smooths are also supported. A Bayesian approach to
     confidence/credible interval calculation is provided. Lower level
     routines for generalized ridge regression and penalized linearly
     constrained least squares are also provided.

Details:

     'mgcv' provides generalized additive modelling functions 'gam',
     'predict.gam' and 'plot.gam', which are very similar in use to the
     S functions of the same name designed by Trevor Hastie.  However
     the underlying representation and estimation of the models is
     based on a penalized regression spline approach, with automatic
     smoothness selection. A number of other functions  such as
     'summary.gam' and 'anova.gam' are also provided,  for extracting
     information from a fitted 'gamObject'.

     Use of 'gam' is much like use of 'glm', except that within a 'gam'
     model formula, isotropic smooths of any number of predictors can
     be specified using 's' terms, while scale invariant smooths of any
     number of predictors can be specified using 'te' terms. Estimation
     is by penalized likelihood or quasi-likelihood maximization, with
     smoothness selection by GCV or gAIC/ UBRE. See 'gam', 'gam.models'
     and 'gam.selection' for some discussion of model specification and
     selection. For detailed control of fitting see 'gam.convergence',
     'gam.method' and 'gam.control'. For checking and visualization see
     'gam.check', 'choose.k', 'vis.gam' and 'plot.gam'. While a number
     of types of smoother are built into the package, it is also
     extendable with user defined smooths, see 'p.spline', for example.

     A Bayesian approach to smooth modelling is used to derive standard
     errors on predictions, and hence credible intervals. The Bayesian
     covariance matrix for the model coefficients is returned in 'Vp'
     of the 'gamObject'. See 'predict.gam' for examples of how this can
     be used to obtain credible regions for any quantity derived from
     the fitted model, either directly, or by direct simulation from
     the posterior distribution of the model coefficients. Frequentist
     approximations can be used for hypothesis testing: see 'anova.gam'
     and 'summary.gam', but note that the underlying approximations are
     not always good in this case.

     The package also provides a generalized additive mixed modelling
     function, 'gamm', based on 'glmmPQL' from the 'MASS' library and
     'lme' from the 'nlme' library. 'gamm' is particularly useful for
     modelling correlated data (i.e. where a simple independence model
     for the residual variation is inappropriate). In addition, low
     level routine 'magic' can fit models to data with a known
     correlation structure.

     Some of the underlying GAM fitting methods are available as low
     level fitting functions: see 'magic' and 'mgcv'. Penalized
     weighted least squares with linear equality and inequality
     constraints is provided by 'pcls'.

     For a complete list of functions type 'library(help=mgcv)'.

Author(s):

     Simon Wood <simon.wood@r-project.org>

     with contributions and/or help from Kurt Hornik, Mike Lonergan,
     Henric Nilsson and Brian Ripley. 

     Maintainer: Simon Wood <simon.wood@r-project.org>

References:

     Wood, S.N. (2006) _Generalized Additive Models: an introduction
     with R_, CRC

Examples:

     ## see examples for gam and gamm

