Covariate Centering and Scaling in Varying-Coefficient Regression with Application to Longitudinal Growth Studies

Abstract

This chapter proposes a class of time-varying coefficient models with centered or standardized covariates, discusses the practical benefits of covariate transformation, and develops a comprehensive set of nonparametric estimation and confidence procedures based on these models. Two popular covariate transformations that are discussed are covariate centering and standardization. It is found that when the covariates strongly depend on time, the local linear estimators or kernel estimators with covariate centering are more stable and have smaller biases than the kernel estimators without covariate centering. As a generalization of the linear and partially linear models, a time-varying coefficient model with the original covariates is presented. It is observed that smoothing estimators based on the popular local least squares, particularly the kernel estimators, may not have desirable theoretical and practical properties when the covariates strongly depend on the time. Estimators for the coefficient curves can be constructed based on a number of smoothing methods, each with its own advantages and disadvantages in practice. It is found that the more general inference approach for longitudinal data is the resampling-subject bootstrap.