Bi-level selection in Longitudinal Analysis with Time Dependent Covariates

Abstract

Penalization methods such as the Lasso (Least absolute shrinkage and selection operator) (Tibshirani 1996) have been used in a variety of contexts to automatically select relevant variables and enhance predictive performance in regression models. Examples are analysis of genetic data and feature selection in image processing. Recently the group Lasso, group bridge, and group MCP have been proposed to deal with group structure in the data. The aim of group Lasso is to select a priori defined groups of variables as a whole. The group bridge and group MCP, in contrast, can perform bi-level selection by encouraging sparse solutions at the group and individual variable levels. In this thesis, we consider the problem of time dependent covariates in longitudinal data analysis to select relevant variable as well as to select the correct lag for each variable. Fu (2003) developed the so-called penalized GEE in longitudinal studies. Since working independent correlation is assumed, this comes do