Generalized Varying Coefficient Models for Longitudinal Data

• Activity Number: 69
• Type: Contributed
• Date/Time: Sunday, August 7, 2005 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Damla Senturk*+ and Hans-Georg Mueller
• Companies: The Pennsylvania State University and University of California, Davis
• Keywords: Functional linear model ; Historical functional linear model ; Longitudinal Data ; Measurement error ; Varying coefficient model

Abstract

We propose a generalization of the varying coefficient model for longitudinal data to cases where only the recent past and/or future times of the predictor processes affect the response at a given time point. More precisely, the targeted regression coefficient functions of the proposed model have sliding window supports around a fixed time point t, and they decay as one gets further away from t. A variant of a recently proposed two-step estimation method for varying coefficient models is proposed for estimation in the context of the generalized varying coefficient models, which is able to handle additive measurement errors in the response and predictors. The proposed method includes two-step procedures, a version of functional linear model, and a version of the historical functional model as special cases. Asymptotic normality results along with proposed consistent estimates of the asymptotic variance yield point-wise asymptotic confidence intervals for the regression coefficients. The proposed model is applied to the problem of predicting serum albumin concentration from recent acute phase protein levels in haemodialysis patients.