Longitudinal Data Model Selection: A Lagrange Optimization Approach

Longitudinal data is widely used in medical science and social science. Models of longitudinal data have also been a popular project in statistics. This paper introduces the basis of longitudinal data and its model structure. In longitudinal data with corre-lated errors, we apply the Lagrange optimization method to obtain a new model selection criterion LOC. We demonstrate that the estimators are consistent when the number of subjects may tend to infinity as the sample size increases. Our simulation studies show that LOC outperforms AIC, BIC and RIC when the sample size is large, because it takes a measure of lack-of-fit as an adaptive penalty, we recommend using LOC when the sample size is large. In contrast, we consider BIC and RIC when the sample size is moderate to large.This dissertation is organized as follows:The first part is the introduction that introduces the basis of this thesis and the current research situation of this topic.In the second part, we introduce the basis of longitudinal data and its model structure.The third part gives several model selection criteria, especially, the Lagrange opti-mization method.The fourth part is the core of the dissertation. In longitudinal data with correlated errors, we apply the Lagrange optimization method to obtain a new model selection crite-rion LOC. We show that the estimators are consistent when the number of subjects may increase to infinity with the sample size.In the fifth part, we provide simulation studies to demonstrate the effectiveness of the proposed criterion.The conclusion and expectation are given at the end of this thesis.