Shape constrained additive models

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 unconstra...

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Bibliographic Details
Published in:Statistics and computing Vol. 25; no. 3; pp. 543 - 559
Main Authors: Pya, Natalya, Wood, Simon N.
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2015
Subjects:
Artificial Intelligence
Convex smoothing
Generalized additive model
Mathematics and Statistics
Monotonic smoothing
P-splines
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
Convex smoothing
P-splines
Monotonic smoothing
Generalized additive model
ISSN:0960-3174, 1573-1375, 1573-1375
Online Access:Get full text
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Summary: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.
ISSN:0960-3174
1573-1375
1573-1375
DOI:10.1007/s11222-013-9448-7