A comparison of methods for the fitting of generalized additive models

Statistics and Computing

Volumn 18, Issue 1, 2008, Pages 87-99

  Binder, Harald ^a   Tutz, Gerhard ^b  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

Boosting; Generalized additive models; Mixed model approach; Selection of smoothness; Variable selection

Indexed keywords

EID: 37249080703     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-007-9040-0     Document Type: Article

References (30)

1. Binder, H., Tutz, G.: Fitting generalized additive models: a comparison of methods. FDM-Preprint 93, University of Freiburg (2006)
2. Breiman, L.: Prediction games and arcing algorithms. Neural Comput. 11, 1493-1517 (1999)
3. Bühlmann, P., Yu, B.: Boosting with the L2 loss: regression and classification. J. Am. Stat. Assoc. 98, 324-339 (2003)
4. Chambers, J.M., Hastie, T.J.: Statistical Models in S. Wadsworth, Pacific Grove (1992)
5. Friedman, J.H.: Greedy function approximation: a gradient boosting machine. Ann. Stat. 29, 1189-1232 (2001)
6. Friedman, J.H., Stuetzle, W.: Projection pursuit regression. J. Am. Stat. Assoc. 76, 817-823 (1981)
7. Friedman, J., Hastie, T., Rosset, S., Tibshirani, R., Zhu, J.: Statistical behavior and consistency of classification methods based on convex risk minimization: discussion of the paper by T. Zhang. Ann. Stat. 32(1), 102-107 (2004)
8. Green, P.J., Silverman, B.W.: Nonparametric Regression and Generalized Linear Models. Chapman & Hall, London (1994)
9. Hand, D.J.: Classifier technology and the illusion of progress. Stat. Sci. 21(1), 1-14 (2006)
10. Hastie, T., Tibshirani, R.: Generalized additive models. Stat. Sci. 1, 295-318 (1986)
11. Hastie, T.J., Tibshirani, R.J.: Generalized Additive Models. Chapman & Hall, London (1990)
12. Hoerl, A.E., Kennard, R.W.: Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1), 55-67 (1970)
13. Hurvich, C.M., Simonoff, J.S., Tsai, C.: Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J. R. Stat. Soc. B 60(2), 271-293 (1998)
14. Kim, Y.-J., Gu, C.: Smoothing spline Gaussian regression: more scalable computation via efficient approximation. J. R. Stat. Soc. B 66(2), 337-356 (2004)
15. Lee, T.C.M.: Smoothing parameter selection for smoothing splines: a simulation study. Comput. Stat. Data Anal. 42, 139-148 (2003)
16. Lindstrom, M.J.: Penlized estimation of free-knot splines. J. Comput. Graph. Stat. 8(2), 333-352 (1999)
17. Linton, O.B., Härdle, W.: Estimation of additive regression models with known links. Biometrika 83, 529-540 (1996)
18. Marx, B.D., Eilers, P.H.C.: Direct generalized additive modelling with penalized likelihood. Comput. Stat. Data Anal. 28, 193-209 (1998)
19. McCullagh, P., Nelder, J.A.: Generalized Linear Models, 2nd edn. Chapman & Hall, London (1989)
20. R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (2006). ISBN 3-900051-07-0
21. Ruppert, D.: Selecting the number of knots for penalized splines. J. Comput. Graph. Stat. 11, 735-757 (2002)
22. Ruppert, D., Wand, M.P., Carroll, R.J.: Semiparametric Regression. Cambridge University Press, Cambridge (2003)
23. Speed, T.: Comment on "That BLUP is a good thing: the estimation of random effects" by G.K. Robinson. Stat. Sci. 6(1), 42-44 (1991)
24. Tibshirani, R.: Regression shrinkage and selection via the lasso. J. R. Stat. Soc. B 58(1), 267-288 (1996)
25. Tutz, G., Binder, H.: Generalized additive modelling with implicit variable selection by likelihood based boosting. Biometrics 62, 961-971 (2006)
26. Wand, M.P.: A comparison of regression spline smoothing procedures. Comput. Stat. 15, 443-462 (2000)
27. Wang, Y.: Mixed effects smoothing spline analysis of variance. J. R. Stat. Soc. B 60(1), 159-174 (1998)
28. Wood, S.N.: Modelling and smoothing parameter estimation with multiple quadratic penalties. J. R. Stat. Soc. B 62(2), 413-428 (2000)
29. Wood, S.N.: Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Am. Stat. Assoc. 99(467), 673-686 (2004)
30. Wood, S.N.: Generalized Additive Models. An Introduction with R. Chapman & Hall/CRC, Boca Raton (2006)