Covariate-adjusted varying coefficient models

Covariate-adjusted regression was recently proposed for situations where both predictors and response in a regression model are not directly observed, but are observed after being contaminated by unknown functions of a common observable covariate. The method has been appealing because of its flexibility in targeting the regression coefficients under different forms of distortion. We extend this methodology proposed for regression into the framework of varying coefficient models, where the goal is to target the covariate-adjusted relationship between longitudinal variables. The proposed method of covariate-adjusted varying coefficient model (CAVCM) is illustrated with an analysis of a longitudinal data set containing calcium absorbtion and intake measurements on 188 subjects. We estimate the age-dependent relationship between these two variables adjusted for the covariate body surface area. Simulation studies demonstrate the flexibility of CAVCM in handling different forms of distortion in the longitudinal setting.     

Generalized varying coefficient models for longitudinal data

We propose a generalization of the varying coefficient modelfor longitudinal data to cases where not only current but alsorecent past values of the predictor process affect current response.More precisely, the targeted regression coefficient functionsof the proposed model have sliding window supports around currenttime t. A variant of a recently proposed two-step estimationmethod for varying coefficient models is proposed for estimationin the context of these generalized varying coefficient models,and is found to lead to improvements, especially for the caseof additive measurement errors in both response and predictors.The proposed methodology for estimation and inference is alsoapplicable for the case of additive measurement error in thecommon versions of varying coefficient models that relate onlycurrent observations of predictor and response processes toeach other. Asymptotic distributions of the proposed estimatorsare derived, and the model is applied to the problem of predictingprotein concentrations in a longitudinal study. Simulation studiesdemonstrate the efficacy of the proposed estimation procedure.     

Estimation of regression models under linear restrictions

The variance-covariance matrices of restricted regression and mixed regression estimators are compared and the consequences of introducing variability in the restrictions are examined.