Costa, M. J. and Shaw, J. Ewart H. (2008) Parametrization and penalties in spline models with an application to survival analysis. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology . (Working papers, Vol.2008).

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Abstract

In this paper we show how a simple parametrization, built from the definition of cubic splines, can aid in the implementation and interpretation of penalized spline models, whatever configuration of knots we choose to use. We call this parametrization value-first derivative parametrization. We perform Bayesian inference by exploring the natural link between quadratic penalties and Gaussian priors. However, a full Bayesian analysis seems feasible only for some penalty functionals. Alternatives include empirical Bayes methods involving model selection type criteria. The proposed methodology is illustrated by an application to survival analysis where the usual Cox model is extended to allow for time-varying regression coefficients.

Item Type:	Working or Discussion Paper (Working Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH):	Spline theory, Knot theory
Series Name:	Working papers
Publisher:	University of Warwick. Centre for Research in Statistical Methodology
Place of Publication:	Coventry
Date:	2008
Volume:	Vol.2008
Number:	No.2
Number of Pages:	19
Status:	Not Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Fundação para a Ciência e a Tecnologia (FCT)
Grant number:	SFRH/BD/16955/2004 (FCT)
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URI:	http://wrap.warwick.ac.uk/id/eprint/35481

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