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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Vydané v:	Statistics and computing Ročník 25; číslo 3; s. 543 - 559
Hlavní autori:	Pya, Natalya, Wood, Simon N.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.05.2015
Predmet:	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
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Abstract	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.
AbstractList	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.
Author	Wood, Simon N. Pya, Natalya
Author_xml	– sequence: 1 givenname: Natalya surname: Pya fullname: Pya, Natalya email: n.y.pya@bath.ac.uk organization: Mathematical Sciences, University of Bath – sequence: 2 givenname: Simon N. surname: Wood fullname: Wood, Simon N. organization: Mathematical Sciences, University of Bath
BackLink	https://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-162090$$DView record from Swedish Publication Index (Umeå universitet)
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Snippet	A framework is presented for generalized additive modelling under shape constraints on the component functions of the linear predictor of the GAM. We represent...
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SubjectTerms	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
Title	Shape constrained additive models
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