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Generalized varying coefficient models for longitudinal data

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  • Damla Şentürk
  • Hans-Georg Müller

Abstract

We propose a generalization of the varying coefficient model for longitudinal data to cases where not only current but also recent past values of the predictor process affect current response. More precisely, the targeted regression coefficient functions of the proposed model have sliding window supports around current time t. A variant of a recently proposed two-step estimation method for varying coefficient models is proposed for estimation in the context of these generalized varying coefficient models, and is found to lead to improvements, especially for the case of additive measurement errors in both response and predictors. The proposed methodology for estimation and inference is also applicable for the case of additive measurement error in the common versions of varying coefficient models that relate only current observations of predictor and response processes to each other. Asymptotic distributions of the proposed estimators are derived, and the model is applied to the problem of predicting protein concentrations in a longitudinal study. Simulation studies demonstrate the efficacy of the proposed estimation procedure. Copyright 2008, Oxford University Press.

Suggested Citation

  • Damla Şentürk & Hans-Georg Müller, 2008. "Generalized varying coefficient models for longitudinal data," Biometrika, Biometrika Trust, vol. 95(3), pages 653-666.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:653-666
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    File URL: http://hdl.handle.net/10.1093/biomet/asn006
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    Cited by:

    1. Şentürk, Damla & Ghosh, Samiran & Nguyen, Danh V., 2014. "Exploratory time varying lagged regression: Modeling association of cognitive and functional trajectories with expected clinic visits in older adults," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 1-15.
    2. Zongwu Cai, 2013. "Functional Coefficient Models for Economic and Financial Data," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    3. Kim, Young-Ju, 2013. "A partial spline approach for semiparametric estimation of varying-coefficient partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 181-187.
    4. Xiao-Feng Wang & Bo Hu & Bin Wang & Kuangnan Fang, 2014. "Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1342-1357, June.
    5. Peixin Zhao & Liugen Xue, 2011. "Variable selection for varying coefficient models with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(2), pages 231-245, September.

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