ABSTRACT
The statistical methods described in the previous chapters are all based on modeling the conditional means of the response variables with various longitudinal variance-covariance structures given time and a set of covariates. The conditional means and the longitudinal variance-covariance structures can be modeled either parametrically or nonparametrically. Although the conditional mean based models are popular in practice, they may be inadequate when the scientific objectives of the study require the evaluation of the conditional distribution functions. We present in this and the subsequent chapters a series of nonparametric models and estimation methods based on the conditional distribution functions. To start from a simple case, this chapter is focused on longitudinal data with time-invariant and categorical covariates, in which case the conditional distribution functions of the outcome variable can be directly estimated through a kernel smoothing method with an unstructured nonparametric model. The more complicated cases for the estimation of conditional distribution functions with time-dependent covariates require some modeling structures which are discussed in Chapters 13, 14 and 15. Throughout these chapters, we define a statistical index, the Rank-Tracking Probability, to measure the temporal tracking ability of a longitudinal variable, and discuss its estimation under various conditional distribution based models.
