Parametrization and penalties in spline models with an application to survival analysis
A simple parametrization, built from the definition of cubic splines, is shown to facilitate the implementation and interpretation of penalized spline models, whatever configuration of knots is used. The parametrization is termed value-first derivative parametrization. Inference is Bayesian and explores 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 inference 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.
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- Hennerfeind, Andrea & Brezger, Andreas & Fahrmeir, Ludwig, 2006. "Geoadditive Survival Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1065-1075, September.
- Thomas Kneib & Ludwig Fahrmeir, 2007. "A Mixed Model Approach for Geoadditive Hazard Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(1), pages 207-228.
- Lu Tian & David Zucker & L.J. Wei, 2005. "On the Cox Model With Time-Varying Regression Coefficients," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 172-183, March.
- Simon N. Wood, 2004. "Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 673-686, January.
- Kauermann, Goran, 2005. "Penalized spline smoothing in multivariable survival models with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 49(1), pages 169-186, April.
- Aldrin, Magne, 2006. "Improved predictions penalizing both slope and curvature in additive models," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 267-284, January.
- S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
- Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
- Brezger, Andreas & Lang, Stefan, 2006. "Generalized structured additive regression based on Bayesian P-splines," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 967-991, February.
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