Fixed and random effects selection in nonparametric additive mixed models

Electronic Journal of Statistics

Volumn 6, Issue , 2012, Pages 810-842

  Lai, Randy C S ^a   Huang, Hsin Cheng ^b   Lee, Thomas C M ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b INSTITUTE OF STATISTICAL SCIENCE   (Taiwan)

Author keywords

Adaptive group lasso; Additive mixed model; Bayesian information criterion; Consistency

Indexed keywords

EID: 84875395305     PISSN: 19357524     EISSN: None     Source Type: Journal    
DOI: 10.1214/12-EJS695     Document Type: Article

References (35)

1. Bondell, H. D., Krishna, A. and Ghosh, S. K. (2010) Joint variable selection for fixed and random effects in linear mixed-effects models., Biometrics, 66, 1069-1077.
2. de Boor, C. (2001), A practical guide to splines. New York: Springer Verlag.
3. Chen, Z. and Dunson, D. B. (2003) Random effects selection in linear mixed models., Biometrics, 59, 762-769.
4. Diggle, P., Heagerty, P., Liang, K. and Zeger, S. (2002), Analysis of longitudinal data. USA: Oxford University Press.
5. Fahrmeir, L. and Lang, S. (2001) Bayesian inference for generalized additive mixed models based on markov random field priors., Applied Statistics, 201-220.
6. Harville, D. A. (1974) Bayesian inference for variance components using only error contrasts., Biometrika, 61, 383-385.
7. Hedeker, D. and Gibbons, R. (2006), Longitudinal data analysis. New York: Wiley.
8. Huang, J., Horowitz, J. and Wei, F. (2010) Variable selection in nonparametric additive models., The Annals of Statistics, 38, 2282-2313.
9. Kinney, S. K. and Dunson, D. B. (2007) Fixed and random effects selection in linear and logistic models., Biometrics, 63, 690-698.
10. Laird, N. and Ware, J. (1982) Random-effects models for longitudinal data., Biometrics, 38, 963-974.
11. Liang, K. and Zeger, S. (1986) Longitudinal data analysis using generalized linear models., Biometrika, 73, 13.
12. Lin, X. and Zhang, D. (1999) Inference in generalized additive mixed models by using smoothing splines., Journal of the Royal Statistical Society Series B, 61, 381-400.
13. Lin, Y. and Zhang, H. (2006) Component selection and smoothing in multivariate nonparametric regression., The Annals of Statistics, 34, 2272.
14. Lindstrom, M. and Bates, D. (1988) Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data., Journal of the American Statistical Association, 1014-1022.
15. Meier, L., van de Geer, S. and Buhlmann, P. (2008) The group lasso for logistic regression., Journal of the Royal Statistical Society Series B, 70, 53.
16. Meier, L., Van de Geer, S., Buhlmann, P. and Zurich, E. (2009) High-dimensional additive modeling., The Annals of Statistics, 37, 3779-3821.
17. Pu, W. and Niu, X.-F. (2006) Selecting mixed-effects models based on a generalized information criterion., JMA, 97, 733-758.
18. Ravikumar, P., Lafferty, J., Liu, H. and Wasserman, L. (2009) Sparse additive models., Journal of the Royal Statistical Society Series B, 71, 1009-1030.
19. Reisby, N., Gram, L., Bech, P., Nagy, A., Petersen, G., Ortmann, J., Ibsen, I., Dencker, S., Jacobsen, O., Krautwald, O., et al. (1977) Imipramine: clinical effects and pharmacokinetic variability. Psychopharmacology, 54, 263-272.
20. Ruppert, D., Wand, M. and Carroll, R. (2003), Semiparametric regression. New York: Cambridge University Press.
21. Shen, X. and Ye, J. (2002) Adaptive model selection., Journal of the American Statistical Association, 97, 210-221.
22. Stone, C. (1985) Additive regression and other nonparametric models., The Annals of Statistics, 13, 689-705.
23. Stone, C. (1986) The dimensionality reduction principle for generalized additive models., The Annals of Statistics, 590-606.
24. Tibshirani, R. (1996) Regression shrinkage and selection via the lasso., Journal of the Royal Statistical Society Series B, 58, 267-288.
25. Van der Vaart, A. and Wellner, J. (1996), Weak convergence and empirical processes: with applications to statistics. New York: Springer Verlag.
26. Van De Geer, S. (2008) High-dimensional generalized linear models and the lasso., The Annals of Statistics, 36, 614.
27. Wand, M. (2003) Smoothing and mixed models., Computational Statistics, 18, 223-250.
28. Wang, H., Li, R. and Tsai, C. (2007a) Tuning parameter selectors for the smoothly clipped absolute deviation method., Biometrika, 94, 553-568.
29. Wang, L., Chen, G. and Li, H. (2007b) Group scad regression analysis for microarray time course gene expression data., Bioinformatics, 23, 1486.
30. Wei, F. and Huang, J. (2008) Consistent group selection in high-dimensional linear regression., Tech. rep., Department of Statistics and Actuarial Science, University of Iowa.
31. Yuan, M. and Lin, Y. (2006) Model selection and estimation in regression with grouped variables., Journal of the Royal Statistical Society Series B, 68, 49-67.
32. Zeger, S. and Liang, K. (1986) Longitudinal data analysis for discrete and continuous outcomes., Biometrics, 42, 121-130.
33. Zhang, D., Lin, X., Raz, J. and Sowers, M. (1998) Semiparametric stochastic mixed models for longitudinal data., Journal of the American Statistical Association, 93.
34. Zhou, S., Shen, X. and Wolfe, D. (1998) Local asymptotics for regression splines and confidence regions., The Annals of Statistics, 26, 1760-1782.
35. Zou, H. (2006) The adaptive lasso and its oracle properties., Journal of the American Statistical Association, 101, 1418-1429.