Penalized Generalized Quasi Likelihood Based Variable Selection for Longitudinal Data
High dimensional longitudinal data with a large number of covariates, have become increasingly common in many bio medical applications. The identification of a sub model that adequately represents the data is necessary for easy interpretation. Also, the inclusion of redundant variables may hinder the accuracy and efficiency of estimation and inference. The joint likelihood function for longitudinal data is challenging, particularly in correlated discrete data. To overcome this problem Wang et al. (Biometrics 68:353 360, 2012) introduced penalized GEEs (PGEEs) with a non convex penalty function which requires only the first two marginal moments and a working correlation matrix. This method works reasonably well in high dimensional problems; however, there is a risk of model mis specification such as variance function and correlation structure and in such situations, we propose variable selection based on penalized generalized quasi likelihood (PGQL) Simulation studies show that when model assumptions are true, the PGQL method has performance comparable with that of PGEEs. However, when the model is mis specified, the PGQL method has clear advantages over the PGEEs method. We have implemented the proposed method in a real case example.