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Marginalized random effects models with ARMA random effects covariance matrix
Journal of the Korean Data & Information Science Society 2018;29:501-12
Published online March 31, 2018
© 2018 Korean Data and Information Science Society.

Dasom Kang1 · Bo Ok Kim2 · Keunbaik Lee3

123Department of Statistics, Sungkyunkwan University
Correspondence to: Associate professor, Department of Statistics, Sungkyunkwan University, Seoul 03063, Korea. E-mail: keunbaik@skku.edu
Received February 17, 2018; Revised March 9, 2018; Accepted March 12, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In longitudinal data analysis, marginalized random effects models (MREMs) have been commonly used when population-averaged effect is of interest (Heagerty, 1999). In the MREMs, modeling of random effects covariance matrix is challenging because the matrix is high-dimensional and the estimate of the covariance matrix should be positive definite. In practice, the covariance matrix is assumed to be autoregressive or exchangeable. However, such structures do not allow more general forms of the serial correlation and it cannot explain heteroscedastic covariance matrices. In this paper, we propose autoregressive and moving average Cholesky decomposition to model the random effects covariance matrix in the MREMs. We analyze lung cancer data using our proposed model.
Keywords : Cholesky decomposition, heterogeneity, longitudinal data, lung cancer study, positive definite.