Open Access
December 2007 Estimation of the covariance matrix of random effects in longitudinal studies
Yan Sun, Wenyang Zhang, Howell Tong
Ann. Statist. 35(6): 2795-2814 (December 2007). DOI: 10.1214/009053607000000523


Longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas. The within cluster correlation structure plays a very important role in longitudinal data analysis. This is because not only can an estimator be improved by incorporating the within cluster correlation structure into the estimation procedure, but also the within cluster correlation structure can sometimes provide valuable insights in practical problems. For example, it can reveal the correlation strengths among the impacts of various factors. Motivated by data typified by a set from Bangladesh pertinent to the use of contraceptives, we propose a random effect varying-coefficient model, and an estimation procedure for the within cluster correlation structure of the proposed model. The estimation procedure is optimization-free and the proposed estimators enjoy asymptotic normality under mild conditions. Simulations suggest that the proposed estimation is practicable for finite samples and resistent against mild forms of model misspecification. Finally, we analyze the data mentioned above with the new random effect varying-coefficient model together with the proposed estimation procedure, which reveals some interesting sociological dynamics.


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Yan Sun. Wenyang Zhang. Howell Tong. "Estimation of the covariance matrix of random effects in longitudinal studies." Ann. Statist. 35 (6) 2795 - 2814, December 2007.


Published: December 2007
First available in Project Euclid: 22 January 2008

zbMATH: 1129.62053
MathSciNet: MR2382666
Digital Object Identifier: 10.1214/009053607000000523

Primary: 62G05
Secondary: 62G08 , 62G20

Keywords: random effects , restricted maximum likelihood estimation , varying-coefficient models , within cluster correlation structure

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • December 2007
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