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Modeling the random effects covariance matrix for generalized linear mixed models. (English) Zbl 1243.62106
Summary: Generalized linear mixed models (GLMMs) are commonly used to analyze longitudinal categorical data. In these models, we typically assume that the random effects covariance matrix is constant across the subject and is restricted because of its high dimensionality and its positive definiteness. However, the covariance matrix may differ by measured covariates in many situations, and ignoring this heterogeneity can result in biased estimates of the fixed effects.
We propose a heterogenous random effects covariance matrix, which depends on covariates, obtained using a modified Cholesky decomposition. This decomposition results in parameters that can be easily modeled without concern that the resulting estimator will not be positive definite. The parameters have a sensible interpretation. We analyze metabolic syndrome data from a Korean Genomic Epidemiology Study using our proposed model.

##### MSC:
 62J12 Generalized linear models (logistic models) 62H12 Estimation in multivariate analysis 62P10 Applications of statistics to biology and medical sciences; meta analysis
##### Keywords:
Cholesky decomposition; longitudinal data; heterogeneity
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##### References:
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