Shape constrained additive models

• DOI: 10.1007/s11222-013-9448-7
• Publication Date: 2014-02-24T10:03:54Z
• Authors: Natalya Pya; Simon N. Wood
• Keywords: Smoothing; Generalized additive model; Additive model; Component (thermodynamics)

A framework is presented for generalized additive modelling under shape constraints on the component functions of linear predictor GAM. We represent constrained model components by mildly non-linear extensions P-splines. Models can contain multiple and unconstrained terms as well multi-dimensional smooths. The considered are sign first or/and second derivatives smooth terms. key advantage approach that it facilitates efficient estimation smoothing parameters an integral part estimation, via GCV or AIC, numerically robust algorithms this presented. also derive simulation free approximate Bayesian confidence intervals components, which shown to achieve close nominal coverage probabilities. Applications using real data examples including risk disease in relation proximity municipal incinerators association between air pollution health.