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Backfitting Random Varying‐Coefficient Models with Time‐Dependent Smoothing Covariates

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  • Hulin Wu
  • Hua Liang

Abstract

. In this paper, we propose a random varying‐coefficient model for longitudinal data. This model is different from the standard varying‐coefficient model in the sense that the time‐varying coefficients are assumed to be subject‐specific, and can be considered as realizations of stochastic processes. This modelling strategy allows us to employ powerful mixed‐effects modelling techniques to efficiently incorporate the within‐subject and between‐subject variations in the estimators of time‐varying coefficients. Thus, the subject‐specific feature of longitudinal data is effectively considered in the proposed model. A backfitting algorithm is proposed to estimate the coefficient functions. Simulation studies show that the proposed estimation methods are more efficient in finite‐sample performance compared with the standard local least squares method. An application to an AIDS clinical study is presented to illustrate the proposed methodologies.

Suggested Citation

  • Hulin Wu & Hua Liang, 2004. "Backfitting Random Varying‐Coefficient Models with Time‐Dependent Smoothing Covariates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 3-19, March.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:1:p:3-19
    DOI: 10.1111/j.1467-9469.2004.00369.x
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    Cited by:

    1. Shuang Wu & Hans-Georg Müller, 2011. "Response-Adaptive Regression for Longitudinal Data," Biometrics, The International Biometric Society, vol. 67(3), pages 852-860, September.
    2. Veerabhadran Baladandayuthapani & Bani K. Mallick & Mee Young Hong & Joanne R. Lupton & Nancy D. Turner & Raymond J. Carroll, 2008. "Bayesian Hierarchical Spatially Correlated Functional Data Analysis with Application to Colon Carcinogenesis," Biometrics, The International Biometric Society, vol. 64(1), pages 64-73, March.
    3. Danh Nguyen & Damla şentürk & Raymond Carroll, 2008. "Covariate-adjusted linear mixed effects model with an application to longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 459-481.
    4. Wang-Li Xu & Li-Xing Zhu, 2009. "A goodness-of-fit test for a varying-coefficients model in longitudinal studies," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(4), pages 427-440.
    5. Xue, Liugen & Xue, Dong, 2011. "Empirical likelihood for semiparametric regression model with missing response data," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 723-740, April.

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