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http://dx.doi.org/10.5351/KJAS.2017.30.1.103

Comparison of the covariance matrix for general linear model  

Nam, Sang Ah (Department of Statistics, Sungkyunkwan University)
Lee, Keunbaik (Department of Statistics, Sungkyunkwan University)
Publication Information
The Korean Journal of Applied Statistics / v.30, no.1, 2017 , pp. 103-117 More about this Journal
Abstract
In longitudinal data analysis, the serial correlation of repeated outcomes must be taken into account using covariance matrix. Modeling of the covariance matrix is important to estimate the effect of covariates properly. However, It is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcome the restrictions, several Cholesky decomposition approaches for the covariance matrix were proposed: modified autoregressive (AR), moving average (MA), ARMA Cholesky decompositions. In this paper we review them and compare the performance of the approaches using simulation studies.
Keywords
longitudinal data analysis; modified Cholesky decomposition; moving average Cholesky decomposition; general linear model;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 Daniels, J. M. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data, Biometrika, 89, 553-566.   DOI
2 Daniels, J. M. and Zhao, Y. D. (2003). Modelling the random effects covariance matrix in longitudinal data, Statistics in Medicine, 22, 1631-1647.   DOI
3 Diggle, P. J., Heagerty, P., Liang, K. Y., and Zeger, S. L. (2002). Analysis of Longitudinal Data (2nd Ed), Oxford University Press, Oxford.
4 Kim, J. and Lee, K. (2015). Survey of models for random effects covariance matrix in generalized linear mixed model, The Korean Journal of Applied Statistics, 28, 211-219.   DOI
5 Kim, J., Sohn, I., and Lee, K. (2016). Bayesian modeling of random effects precision/covariance matrix in cumulative logit random effects models, Communications for Statistical Applications and Methods, 24, 81-96.
6 Lee, K. (2013). Bayesian modeling of random effects covariance matrix for generalized linear mixed models, Communications for Statistical Applications and Methods, 20, 235-240.   DOI
7 Lee, K., Baek, C., and Daniels, M. J. (2017). ARMA Cholesky factor models for the covariance matrix of linear models, Computational Statistics & Data Analysis, working paper.
8 Lee, K. and Sung, S. A. (2014). Autoregressive Cholesky factor modeling for marginalized random effects models, Communications for Statistical Applications and Methods, 21, 169-181.   DOI
9 Lee, K. and Yoo, J. (2014). Bayesian Cholesky factor models in random effects covariance matrix for generalized linear mixed models, Computational Statistics & Data Analysis, 80, 111-116.   DOI
10 Lee, K., Yoo, J. K., Lee, J., and Hagan, J. (2012). Modeling the random effects covariance matrix for the generalized linear mixed models, Computational Statistics & Data Analysis, 56, 1545-1551.   DOI
11 Pan, J. X. and Mackenzie, G. (2003). Model selection for joint mean-covariance structures in longitudinal studies. Biometrika, 90, 239-244.   DOI
12 Pan, J. X. and MacKenzie, G. (2006). Regression models for covariance structures in longitudinal studies. Statistical Modelling, 6, 43-57.   DOI
13 Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisation, Biometrika, 86, 677-690.   DOI
14 Pourahmadi, M. (2000). Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix, Biometrika, 87, 425-435.   DOI
15 Zhang, W. and Leng, C. (2012). A moving average Cholesky factor model in covariance modeling for longitudinal data, Biometrika, 99, 141-150.   DOI