Shape constrained additive models
Shape constrained additive models
复制标题
DOI：
10.1007/s11222-013-9448-7
复制
发表时间：
2015-05-01
影响因子：
2.2
通讯作者：
Wood, Simon N.
中科院分区：
文献类型：
--
作者：
Pya, Natalya;Wood, Simon N.
在形状约束下，在GAM的线性预测因子的组件函数上提出了一个框架。我们通过P-Splines的轻度非线性扩展代表形状约束模型组件。模型可以包含多个形状约束和不受约束的项以及形状约束的多维平滑词。所考虑的约束在于第一个或/和平滑项的第二个衍生物的符号。该方法的一个关键优点是，它通过GCV或AIC促进了对平滑参数的有效估计，作为模型估计的组成部分，并为此提供了数值强大的算法。我们还为光滑组件得出了仿真的无模拟近似贝叶斯置信区间，这些阳台成分显示出接近名义覆盖概率。使用真实的数据示例提出了申请，包括与市政焚化炉的接近性以及空气污染与健康之间的关联。
A framework is presented for generalized additive modelling under shape constraints on the component functions of the linear predictor of the GAM. We represent shape constrained model components by mildly non-linear extensions of P-splines. Models can contain multiple shape constrained and unconstrained terms as well as shape constrained multi-dimensional smooths. The constraints considered are on the sign of the first or/and the second derivatives of the smooth terms. A key advantage of the approach is that it facilitates efficient estimation of smoothing parameters as an integral part of model estimation, via GCV or AIC, and numerically robust algorithms for this are presented. We also derive simulation free approximate Bayesian confidence intervals for the smooth components, which are shown to achieve close to nominal coverage probabilities. Applications are presented using real data examples including the risk of disease in relation to proximity to municipal incinerators and the association between air pollution and health.