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Biometrika Advance Access originally published online on June 13, 2008
Biometrika 2008 95(3):653-666; doi:10.1093/biomet/asn006
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© 2008 Biometrika Trust

Articles

Generalized varying coefficient models for longitudinal data

Damla Sentürk

Department of Statistics, Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A. dsenturk{at}stat.psu.edu

Hans-Georg Müller

Department of Statistics, University of California, Davis, California 95616, U.S.A. mueller{at}wald.ucdavis.edu

Received for publication 1 July 2006. Revision received 1 November 2007.
  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.

Key Words: Linear regression • Measurement error model • Prediction • Smoothing • Two-step procedure


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