Statistics and Its Interface

Volume 12 (2019)

Number 3

Analysis of longitudinal data by combining multiple dynamic covariance models

Pages: 479 – 487



Lin Xu (School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou, China)

Man-Lai Tang (Department of Mathematics and Statistics, Hang Seng University of Hong Kong)

Ziqi Chen (School of Mathematics and Statistics, Central South University, Changsha, China)


In longitudinal data analysis, it is crucial to understand the dynamic of the covariance matrix of repeated measurements and correctly model it in order to achieve efficient estimators of the mean regression parameters. It is well known that any incorrect covariance matrices can result in inefficient estimators of the mean regression parameters. In this article, we propose an empirical likelihood based method which combines the advantages of different dynamic covariance modeling approaches. The effectiveness of the proposed approach is demonstrated by an anesthesiology dataset and some simulation studies.


empirical likelihood, longitudinal data analysis, maximum likelihood, modified Cholesky decomposition, multiple covariance models

The research of Dr. Chen was supported by NSFC grant 11871477 and Hunan Provincial Natural Science Foundation of China 2016JJ3138.

Dr. Xu’s research was supported by Zhejiang Provincial NSF of China grant LY19A010006, Zhejiang Federation of Humanities and Social Sciences Circles grant 16NDJC154YB and First Class Discipline of Zhejiang–A (Zhejiang University of Finance and Economics- Statistics).

Dr. Tang’s research was supported by a grant from the Research Grant Council of the Hong Kong Special Administrative Region (Project No. UGC/FDS14/P01/16), a grant from National Natural Science Foundation of China (Grant No. 11871124), and the Big Data and Artificial Intelligence Group of School of Decision Sciences.

Received 17 March 2018

Published 4 June 2019