R: Shape Constrained Additive Models

scam-package {scam} | R Documentation

## Shape Constrained Additive Models

### Description

`scam` provides functions for generalized additive modelling under shape constraints on the component functions of the linear predictor of the GAM. Models can contain multiple shape constrained and unconstrained terms as well as bivariate smooths with double or single monotonicity. Univariate smooths under eight possible shape constraints such as monotonically increasing/decreasing, convex/concave, increasing/decreasing and convex, increasing/decreasing and concave, are available as model terms.

The model set up is the same as in `gam()` in package `mgcv` with the added shape constrained smooths, so the unconstrained smooths can be of more than one variable, and other user defined smooths can be included. Penalized log likelihood maximization is used to fit the model together with the automatic smoothness selection.

### Details

Package: | scam
Version: | 1.2-12
Author: | Natalya Pya <nat.pya@gmail.com>
Maintainer: | Natalya Pya <nat.pya@gmail.com>
Title: | Shape Constrained Additive Models
Date: | 2021-08-10
Description: | Routines for generalized additive modelling under shape constraints on the component functions of the linear predictor (Pya and Wood, 2015) <doi:10.1007/s11222-013-9448-7>. Models can contain multiple shape constrained (univariate and/or bivariate) and unconstrained terms. The routines of gam() in package 'mgcv' are used for setting up the model matrix, printing and plotting the results. Penalized likelihood maximization based on Newton-Raphson method is used to fit a model with multiple smoothing parameter selection by GCV or UBRE/AIC.
Depends: | R (>= 2.15.0), mgcv (>= 1.8-2)
Imports: | methods, stats, graphics, Matrix, splines
Suggests: | nlme
License: | GPL (>= 2)
LazyLoad: | yes

The package provides generalized additive modelling under shape constraints on the component functions of the linear predictor. `scam` and `plot.scam` functions are based on the functions of the unconstrained GAM `gam()` and `plot.gam()` in package `mgcv` and similar in use. `summary.scam` allows to extract the results of the model fitting in the same way as in `summary.gam`. A Bayesian approach is used to obtain a covariance matrix of the model coefficients and credible intervals for each smooth.

### Author(s)

Natalya Pya <nat.pya@gmail.com> based partly on `mgcv` by Simon Wood

Maintainer: Natalya Pya <nat.pya@gmail.com>

### References

Pya, N. and Wood, S.N. (2015) Shape constrained additive models. Statistics and Computing, 25(3), 543-559

Pya, N. (2010) Additive models with shape constraints. PhD thesis. University of Bath. Department of Mathematical Sciences

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

Wood, S.N. (2008) Fast stable direct fitting and smoothness selection for generalized additive models. Journal of the Royal Statistical Society (B) 70(3):495-518

Wood, S.N. (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society (B) 73(1):3-36

The package was part supported by EPSRC grants EP/I000917/1, EP/K005251/1 and the Science Committee of the Ministry of Science and Education of the Republic of Kazakhstan grant #2532/GF3.

### Examples

    ## see examples for scam

[Package scam version 1.2-12 Index]