mgcv provides functions for generalized additive modelling and
generalized additive mixed modelling. 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.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).
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