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Longitudinal data analysis using sufficient dimension reduction method

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  • Li, Lexin
  • Yin, Xiangrong

Abstract

There have been an increasing number of applications where the number of predictors is large, meanwhile data are repeatedly measured at a sequence of time points. In this article we investigate how dimension reduction method can be employed for analyzing such high-dimensional longitudinal data. Predictor dimension can be effectively reduced while full regression means information can be retained during dimension reduction. Simultaneous variable selection along with dimension reduction is studied, and graphical diagnosis and model fitting after dimension reduction are investigated. The method is flexible enough to encompass a variety of commonly used longitudinal models.

Suggested Citation

  • Li, Lexin & Yin, Xiangrong, 2009. "Longitudinal data analysis using sufficient dimension reduction method," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4106-4115, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4106-4115
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    References listed on IDEAS

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    1. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    2. Liqiang Ni & R. Dennis Cook & Chih-Ling Tsai, 2005. "A note on shrinkage sliced inverse regression," Biometrika, Biometrika Trust, vol. 92(1), pages 242-247, March.
    3. Howard D. Bondell & Lexin Li, 2009. "Shrinkage inverse regression estimation for model‐free variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 287-299, January.
    4. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    5. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    6. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    7. Wang, Qin & Yin, Xiangrong, 2008. "Sufficient dimension reduction and variable selection for regression mean function with two types of predictors," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2798-2803, November.
    8. Lin D Y & Ying Z, 2001. "Semiparametric and Nonparametric Regression Analysis of Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 103-126, March.
    9. Wenjiang J. Fu, 2003. "Penalized Estimating Equations," Biometrics, The International Biometric Society, vol. 59(1), pages 126-132, March.
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