Estimation of Varying Coefficients for a Growth Curve Model

Abstract

In this paper, a new approach of modelling growth curves is developed which uses time-varying coefficients. Since the mean structure of the growth curve model has many unknown parameters depending on both covariates and time trend designs, it can be difficult to understand and interpret estimated parameters. Using varying coefficient functions, the effects of covariates can be evaluated and visualized more easily. The asymptotic functional confidence intervals are derived theoretically and a procedure is proposed to test whether the effects of covariates are significant.