Practical variable selection for generalized additive models

Computational Statistics and Data Analysis

Volumn 55, Issue 7, 2011, Pages 2372-2387

  Marra, Giampiero ^a   Wood, Simon N ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b University of Bath   (United Kingdom)

Author keywords

Generalized additive model; Nonnegative garrote estimator; Penalized thin plate regression spline; Practical variable selection; Shrinkage smoother

Indexed keywords

BETA CAROTENE; COMPONENT SELECTION; COVARIATES; CROSS-SECTIONAL STUDY; EMPIRICAL PERFORMANCE; EXHAUSTIVE SEARCH; EXTENSIVE SIMULATIONS; GENERALIZED ADDITIVE MODEL; NONNEGATIVE GARROTE ESTIMATOR; NONPARAMETRIC TESTING; PENALIZED THIN PLATE REGRESSION SPLINE; PRACTICAL GUIDELINES; PRACTICAL VARIABLE SELECTION; SELECTION PROCEDURES; SINGLE-STEP; VARIABLE SELECTION;

SHRINKAGE; SPLINES;

ESTIMATION;

EID: 79953654016     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2011.02.004     Document Type: Article

References (44)

1. M. Avalos, Y. Grandvalet, and C. Ambroise Parsimonious additive models Computational Statistics and Data Analysis 51 2007 2851 2870 (Pubitemid 46186558)
2. C. Belitz, and S. Lang Simultaneous selection of variables and smoothing parameters in structured additive regression models Computational Statistics and Data Analysis 51 2008 6044 6059
3. H. Binder, and G. Tutz A comparison of methods for the fitting of generalized additive models Statistics and Computing 18 2008 87 99
4. L. Breiman Better subset regression using the nonnegative garrote Technometrics 37 1995 373 384
5. P. Bhlmann, and T. Hothorn Twin boosting: improved feature selection and prediction Statistics and Computing 20 2010 119 138
6. P. Bhlmann, and B. Yu Boosting with the L2 loss: regression and classification Journal of the American Statistical Association 98 2003 324 339
7. E. Cantoni, J. Flemming, and E. Ronchetti Variable selection in additive models by nonnegative garrote Statistical Modelling 11 2011 165 180
8. E. Cantoni, and T. Hastie Degrees of freedom tests for smoothing splines Biometrika 89 2002 251 263 (Pubitemid 41311979)
9. S. Chib, and E. Greenberg Semiparametric modeling and estimation of instrumental variable models Journal of Computational and Graphical Statistics 16 2007 86 114
10. Z.J. Daye, and X.J. Jeng Shrinkage and model selection with correlated variables via weighted fusion Computational Statistics and Data Analysis 53 2009 1284 1298
11. B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani Least angle regression The Annals of Statistics 32 2004 407 451
12. J.E. Gentle Random Number Generation and Monte Carlo Methods 2003 Springer-Verlag
13. Greven, S., Kneib, T., 2009. On the behavior of marginal and conditional Akaike information criteria in linear mixed models. Johns Hopkins University, Department of Biostatistics Working Papers. Paper 179.
14. A. Guisan, T.C. Edwards, and T. Hastie Generalized linear and generalized additive models in studies of species distributions: setting the scene Ecological Modelling 157 2002 89 100 (Pubitemid 35255408)
15. W. Hrdle, P. Hall, and J.S. Marron How far are automatically chosen regression smoothing parameters from their optimum? Journal of the American Statistical Association 83 1988 86 95
16. T. Hastie, and R. Tibshirani Generalized Additive Models 1990 Chapman & Hall London
17. l 1 penalized regression: a review Statistics Surveys 2 2008 61 93
18. G. Kauermann, G. Claeskens, and J.D. Opsomer Bootstrapping for penalized spline regression Journal of Computational and Graphical Statistics 18 2009 126 146
19. G. Kauermann, and G. Tutz Testing generalized linear and semiparametric models against smooth alternatives Journal of the Royal Statistical Society Series B 63 2001 147 166 (Pubitemid 33392468)
20. G. Kimeldorf, and G. Wahba A correspondence between Bayesian estimation of stochastic processes and smoothing by splines Annals of Mathematical Statistics 41 1970 495 502
21. Y. Lin, and H.H. Zhang Component selection and smoothing in multivariate nonparametric regression Annals of Statistics 34 2006 2272 2297
22. G. Marra, and R. Radice Penalised regression splines: theory and application to medical research Statistical Methods in Medical Research 19 2010 107 125
23. P. McCullagh, and J.A. Nelder Generalized Linear Models 1989 Chapman & Hall London
24. D.W. Nierenberg, T.A. Stukel, J.A. Baron, B.J. Dain, and E.R. Greenberg The skin cancer prevention study group. Determinants of plasma levels of beta-carotene and retinol American Journal of Epidemiology 130 1989 511 521 (Pubitemid 19214618)
25. D.J. Nott, and C. Leng Bayesian projection approaches to variable selection in generalized linear models Computational Statistics and Data Analysis 54 2010 3227 3241
26. R Development Core Team, 2010. R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN: 3-900051-07-0. URL: http://www.R-project.org.
27. P.T. Reiss, and R.T. Ogden Smoothing parameter selection for a class of semiparametric linear models Journal of the Royal Statistical Society Series B 71 2009 505 524
28. F. Scheipl, S. Greven, and H. Kuchenhoff Size and power of tests for a zero random effect variance or polynomial regression in additive and linear mixed models Computational Statistics and Data Analysis 52 2008 3283 3299
29. N. Shafik, and G. Tutz Boosting nonlinear additive autoregressive time series Computational Statistics and Data Analysis 53 2009 2453 2464
30. T. Simil, and J. Tikka Input selection and shrinkage in multiresponse linear regression Computational Statistics and Data Analysis 52 2007 406 422 (Pubitemid 47331720)
31. R. Tibshirani Regression shrinkage and selection via the lasso Journal of the Royal Statistical Society Series B 58 1996 267 288
32. G. Tutz, and H. Binder Generalized additive modeling with implicit variable selection by likelihood-based boosting Biometrics 62 2006 961 971
33. G. Tutz, and H. Binder Boosting ridge regression Computational Statistics and Data Analysis 51 2007 6044 6059 (Pubitemid 47126005)
34. C. Wager, F. Vaida, and G. Kauermann Model selection for penalized spline smoothing using akaike information criteria Australian and New Zealand Journal of Statistics 49 2007 173 190
35. G. Wahba A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem The Annals of Statistics 13 1985 1378 1402
36. S.N. Wood Thin plate regression splines Journal of the Royal Statistical Society Series B 65 2003 95 114 (Pubitemid 37155338)
37. S.N. Wood Generalized Additive Models: An Introduction with R 2006 Chapman & Hall London
38. S.N. Wood Fast stable direct fitting and smoothness selection for generalized additive models Journal of the Royal Statistical Society Series B 70 2008 495 518
39. S.N. Wood Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models Journal of the Royal Statistical Society Series B 73 2011 3 36
40. L. Xue Consistent variable selection in additive models Statistica Sinica 19 2009 1281 1296
41. Yuan, M., 2007. Nonnegative garrote component selection in functional anova models. In: Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics. Puerto Rico.
42. M. Yuan, and Y. Lin Model selection and estimation in regression with grouped variables Journal of the Royal Statistical Society Series B 68 2006 49 67 (Pubitemid 43415335)
43. H.H. Zhang, and Y. Lin Component selection and smoothing for nonparametric regression in exponential families Statistica Sinica 16 2006 1021 1041 (Pubitemid 44744361)
44. H. Zou The adaptive LASSO and its oracle properties Journal of the American Statistical Association 101 2006 1418 1429