# R: GAMs with GCV smoothness estimation and GAMMs by REML/PQL

mgcv-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

[Package mgcv version 1.3-27 Index]