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Shape constrained additive models
2015 (English)In: Statistics and computing, ISSN 0960-3174, E-ISSN 1573-1375, Vol. 25, no 3, p. 543-559Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2015. Vol. 25, no 3, p. 543-559
Keywords [en]
Monotonic smoothing, Convex smoothing, Generalized additive model, P-splines
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-162090DOI: 10.1007/s11222-013-9448-7ISI: 000352705000004OAI: oai:DiVA.org:umu-162090DiVA, id: diva2:1342530
Available from: 2019-08-13 Created: 2019-08-13 Last updated: 2019-08-15Bibliographically approved

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Pya, Natalya
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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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Output format
  • html
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