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Poisson linear mixed models with ARMA random effects covariance matrix
Journal of the Korean Data & Information Science Society 2017;28:927-36
Published online July 31, 2017
© 2017 Korean Data & Information Science Society.

Jiin Choi1 · Keunbaik Lee2

12Department of Statistics, Sungkyunkwan University
Correspondence to: Keunbaik Lee
Associate professor, Department of Statistics, Sungkyunkwan University, Seoul 110-745, Korea. E-mail:
Received June 24, 2017; Revised July 17, 2017; Accepted July 20, 2017.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
To analyze longitudinal count data, Poisson linear mixed models are commonly used. In the models the random effects covariance matrix explains both within-subject variation and serial correlation of repeated count outcomes. When the random effects covariance matrix is assumed to be misspecified, the estimates of covariates effects can be biased. Therefore, we propose reasonable and exible structures of the covariance matrix using autoregressive and moving average Cholesky decomposition (ARMACD). The ARMACD factors the covariance matrix into generalized autoregressive parameters (GARPs), generalized moving average parameters (GMAPs) and innovation variances (IVs). Positive IVs guarantee the positive-definiteness of the covariance matrix. In this paper, we use the ARMACD to model the random effects covariance matrix in Poisson loglinear mixed models. We analyze epileptic seizure data using our proposed model.
Keywords : Cholesky decomposition, general linear mixed model, high dimensionality, longitudinal count data, positive-definite