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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