Estimating Varying Coefficients for Longitudinal Data without Specifying Spatial-Temporal Baseline Trend

In this paper we develop a method for estimating varying coefficients on effects of covariates without modeling the shape of the spatial-temporal baseline trend. We consider the situation where primary interest is in the effects of covariates and the spatial-temporal baseline trend, though non-negligible, is of secondary interest. This is similar to the situation with the Cox proportional hazards model in survival analysis. Basis functions are used to model the shapes of the varying coefficients, but no particular shape is assumed for the spatial-temporal baseline trend. After the effects of covariates are evaluated, estimates of the spatial-temporal baseline trend can be obtained nonparametrically.