Increasing the usefulness of additive spline models by knot removal
Modern techniques for fitting generalized additive models mostly rely on basis expansions of covariates using a large number of basis functions and penalized estimation of parameters. For example, a mixed model approach is used to fit a model for children's lung function that allows for non-linear influence of several covariates available in a substantial data set. While the resulting model is expected to have good prediction performance, its handling beyond simple visual presentation is problematic. It is shown how the number basis functions of the underlying B-spline representation can be reduced by knot removal techniques without refitting, while preserving the shape of the fitted functions. The condition for exact knot removal is extended towards approximate knot removal by incorporating the covariance matrix of the initial parameter estimates, resulting in considerable simplification of the model. Covariance matrices for the transformed parameter estimates are provided. It is demonstrated that enforcing the knot removal condition during estimation leads to the difference penalties employed in the P-spline approach for estimation of B-spline coefficients, and therefore provides a further justification for this type of penalty. A final transform to a truncated power basis provides a simple equation for the model. This increases transportability, while retaining properties of the initial fit such as good prediction performance.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
- Zhou S. & Shen X., 2001. "Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 247-259, 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.
- W. Sauerbrei & P. Royston, 1999. "Building multivariable prognostic and diagnostic models: transformation of the predictors by using fractional polynomials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(1), pages 71-94.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, November.
- Breiman, Leo, 1993. "Fitting additive models to regression data : Diagnostics and alternative views," Computational Statistics & Data Analysis, Elsevier, vol. 15(1), pages 13-46, January.
- Daniel Gervini, 2006. "Free-knot spline smoothing for functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 671-687.
- Wenxin Mao & Linda H. Zhao, 2003. "Free-knot polynomial splines with confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 901-919.
- Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, November.
- Molinari, Nicolas & Durand, Jean-Francois & Sabatier, Robert, 2004. "Bounded optimal knots for regression splines," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 159-178, March.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:12:p:5305-5318. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.