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 univariate and bivariate shape constrained terms, unconstrained terms and parametric terms. A wide variety of shape constrained smooths covered in shape.constrained.smooth.terms are provided.
The model set-up is similar to that of gam() of the package mgcv, so unconstrained smooths of one or more variables of the mgcv can be included in SCAMs. User-defined smooths can be added as well. SCAM is estimated by penalized log likelihood maximization and provides automatic smoothness selection by minimizing generalized cross validation or similar. A Bayesian approach is used to obtain a covariance matrix of the model coefficients and credible intervals for each smooth. Linear functionals of smooth functions with shape constraints, parametric model terms, simple linear random effects terms, bivariate interaction smooths with increasing/decreasing constraints (smooth ANOVA), and identity link Gaussian models with AR1 residuals are supported.
tools:::Rd_package_author("scam") based partly on mgcv by Simon Wood
Maintainer: tools:::Rd_package_maintainer("scam")
scam provides generalized additive modelling under shape constraints functions scam, summary.scam, plot.scam, scam.check, predict.scam, anova.scam, and vis.scam. These are based on the functions of the unconstrained GAM of the package mgcv and are similar in use.
The use of scam() is much like the use of gam(), except that within a scam model formula, shape constrained smooths of one or two predictors can be specified using s terms with a type of shape constraints used specified as a letter character string of the argument bs, e.g. s(x, bs="mpi") for smooth subject to increasing constraint. See shape.constrained.smooth.terms for a complete overview of what is available. scam model estimation is performed by penalized likelihood maximization, with smoothness selection by GCV, UBRE/AIC criteria. See scam, linear.functional.terms for a short discussion of model specification and some examples. See scam arguments optimizer and optim.method, and scam.control for detailed control of scam model fitting. For checking and visualization, see scam.check, plot.scam, qq.scam and vis.scam. For extracting fitting results, see summary.scam and anova.scam.
A Bayesian approach to smooth modelling is used to obtain covariance matrix of the model coefficients and credible intervals for each smooth. Vp element of the fitted object of class scam returns the Bayesian covariance matrix, Ve returns the frequentist estimated covariance matrix for the parameter estimators. The
frequentist estimated covariance matrix for the reparametrized parameter estimators (obtained using the delta method) is returned in Ve.t, which is particularly useful for testing individual smooth
terms for equality to the zero function (not so useful for CI's as smooths are usually biased).
Vp.t returns the Bayesian covariance matrix for the reparametrized parameters. Frequentist approximations can be used for hypothesis testing based on model comparison; see anova.scam and summary.scam for info on hypothesis testing.
For a complete list of functions type library(help=scam).
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. (2017) Generalized Additive Models: An Introduction with R (2nd edition). 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.