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.
scam
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.
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.
# NOT RUN {
## see examples for scam
# }
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