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Bayesian Cholesky factor models in random effects covariance matrix for generalized linear mixed models

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  • Lee, Keunbaik
  • Yoo, Jae Keun

Abstract

Random effects in generalized linear mixed models (GLMM) are used to explain the serial correlation of the longitudinal categorical data. Because the covariance matrix is high dimensional and should be positive definite, its structure is assumed to be constant over subjects and to be restricted such as AR(1) structure. However, these assumptions are too strong and can result in biased estimates of the fixed effects. In this paper we propose a Bayesian modeling for the GLMM with regression models for parameters of the random effects covariance matrix using a moving average Cholesky decomposition which factors the covariance matrix into moving average (MA) parameters and IVs. We analyze lung cancer data using our proposed model.

Suggested Citation

  • Lee, Keunbaik & Yoo, Jae Keun, 2014. "Bayesian Cholesky factor models in random effects covariance matrix for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 111-116.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:111-116
    DOI: 10.1016/j.csda.2014.06.016
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    References listed on IDEAS

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    1. Lee, Keunbaik & Lee, JungBok & Hagan, Joseph & Yoo, Jae Keun, 2012. "Modeling the random effects covariance matrix for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1545-1551.
    2. Jianxin Pan, 2003. "On modelling mean-covariance structures in longitudinal studies," Biometrika, Biometrika Trust, vol. 90(1), pages 239-244, March.
    3. M. Pourahmadi & M. J. Daniels, 2002. "Dynamic Conditionally Linear Mixed Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 58(1), pages 225-231, March.
    4. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    5. Weiping Zhang & Chenlei Leng, 2012. "A moving average Cholesky factor model in covariance modelling for longitudinal data," Biometrika, Biometrika Trust, vol. 99(1), pages 141-150.
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    Cited by:

    1. Tsukuma, Hisayuki, 2016. "Minimax estimation of a normal covariance matrix with the partial Iwasawa decomposition," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 190-207.
    2. Keunbaik Lee & Hoimin Jung & Jae Keun Yoo, 2019. "Modeling of the ARMA random effects covariance matrix in logistic random effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 281-299, June.
    3. Lee, Keunbaik & Baek, Changryong & Daniels, Michael J., 2017. "ARMA Cholesky factor models for the covariance matrix of linear models," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 267-280.

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