ABSTRACT
This chapter is concerned with the time-varying coefficient models with timevarying covariates. Unlike the special case in Chapter 6, where the covariates are time-invariant, the covariate effects described in this chapter are instantaneous in the sense that the model only describes the relationship between the covariates and the outcome at the same time. Despite this simplification, the time-varying coefficient models discussed in this chapter can be widely applied in practical longitudinal studies, because these models have the simple interpretation as being linear models at a specific given time point. The changing coefficient values at different time points allow the models to vary over time, which adds flexibility to the models. The coefficient curves of the models can be estimated by a number of different approaches, each with its own advantages and disadvantages. The estimation methods presented in this chapter are based on a one-step local least squares approach, which has the advantage of being conceptually simple. Additional local and global estimation methods for the same models and data structure are presented in Chapters 8 and 9.
