Longitudinal Data Models with Nonparametric Random Effect Distributions

Abstract

There is the saying which says you cannot see the woods for the trees. This thesis aims to circumvent this unfortunate situation: Longitudinal data on tree growth, as an example of multiple observations of similar individuals pooled together in one data set, are modeled simultaneously rather than each individual separately. This is done under the assumption that one model is suitable for all individuals but its parameters vary following un- known nonparametric random effect distributions. The goal is a maximum likelihood estimation of these distributions considering all provided data and using basis-spline-approximations for the densities of each distribution func- tion over the same spline-base. The implementation of all procedures is carried out in R and attached to this thesis.