Joint Variable Selection of Mean-Covariance Model for Longitudinal Data

Dengke Xu, Zhongzhan Zhang, Liucang Wu

College of Applied Sciences, Beijing University of Technology, Beijing, China.
Faculty of Science, Kunming University of Science and Technology, Kunming, China.

DOI: 10.4236/ojs.2013.31004                

Abstract

In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.

Keywords

Joint Mean and Covariance Models; Variable Selection; Cholesky Decomposition; Longitudinal Data; Penalized Maximum Likelihood Method

Conflicts of Interest

The authors declare no conflicts of interest.

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