Bayesian Modeling of Random Effects Covariance Matrix for Generalized Linear Mixed Models

- Journal title : Communications for Statistical Applications and Methods
- Volume 20, Issue 3, 2013, pp.235-240
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CSAM.2013.20.3.235

Title & Authors

Bayesian Modeling of Random Effects Covariance Matrix for Generalized Linear Mixed Models

Lee, Keunbaik;

Lee, Keunbaik;

Abstract

Generalized linear mixed models(GLMMs) are frequently used for the analysis of longitudinal categorical data when the subject-specific effects is of interest. In GLMMs, the structure of the random effects covariance matrix is important for the estimation of fixed effects and to explain subject and time variations. The estimation of the matrix is not simple because of the high dimension and the positive definiteness; subsequently, we practically use the simple structure of the covariance matrix such as AR(1). However, this strong assumption can result in biased estimates of the fixed effects. In this paper, we introduce Bayesian modeling approaches for the random effects covariance matrix using a modified Cholesky decomposition. The modified Cholesky decomposition approach has been used to explain a heterogenous random effects covariance matrix and the subsequent estimated covariance matrix will be positive definite. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using these methods.

Keywords

Modified Cholesky decomposition;heterogeneity;Positive definiteness;

Language

English

Cited by

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References

1.

Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 125-134.

2.

Celeux, G., Forbes, F., Robert, C. P. and Titterington, D. M. (2006). Deviance information criteria for missing data models, Bayesian Analysis, 1, 651-674.

3.

Daniels, M. J. and Hogan, J.W. (2008). Missing Data in Longitudinal Studies: Strategies for Bayesian Modeling and Sensitivity Analysis, Chapman & Hall/CRC.

4.

Daniels, J. M. and Pourahmadi, M. (2002). Bayesian analysis of covariance matrices and dynamic models for longitudinal data, Biometrika, 89, 553-566.

5.

Daniels, J. M. and Zhao, Y. D. (2003). Modelling the random effects covariance matrix in longitudinal data, Statistics in Medicine, 22, 1631-1647.

6.

Heagerty, P. J. and Kurland, B. F. (2001). Misspecified maximum likelihood estimates and generalized linear mixed models, Biometrika, 88, 973-985.

7.

Kim, J., Kim, E., Yi, H., Joo, S., Shin, K., Kim, J., Kim, K. and Shin, C. (2006). Short-term incidence rate of hypertension in Korea middle-aged adults, Journal of Hypertension, 24, 2177-2182.

8.

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.

9.

Pan, J. and Mackenzie, G. (2003). On modelling mean-covariance structures in longitudinal studies, Biometrika, 90, 239-244.

10.

Pan, J. and Mackenzie, G. (2006). Regression models for covariance structures in longitudinal studies, Statistical Modelling, 6, 43-57.

11.

Pourahmadi, M. (1999). Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation, Biometrika, 86, 677-690.

12.

Pourahmadi, M. (2000). Maximum likelihood estimation of generalized linear models for multivariate normal covariance matrix, Biometrika, 87, 425-435.