TY - JOUR
T1 - Modeling the random effects covariance matrix for generalized linear mixed models
AU - Lee, Keunbaik
AU - Lee, Jungbok
AU - Hagan, Joseph
AU - Yoo, Jae Keun
N1 - Funding Information:
The authors are grateful to three referees for many helpful comments. For the corresponding author Jae Keun Yoo, this work was supported by Basic Science Research Program through the National Research Foundation of Korea (KRF) funded by the Ministry of Education, Science and Technology ( 2011-0005581 ).
PY - 2012/6
Y1 - 2012/6
N2 - 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. In this paper, we propose a heterogenous random effects covariance matrix, which depends on covariates, obtained using the 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.
AB - 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. In this paper, we propose a heterogenous random effects covariance matrix, which depends on covariates, obtained using the 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.
KW - Cholesky decomposition
KW - Heterogeneity
KW - Longitudinal data
UR - http://www.scopus.com/inward/record.url?scp=84857646089&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2011.09.011
DO - 10.1016/j.csda.2011.09.011
M3 - Article
AN - SCOPUS:84857646089
SN - 0167-9473
VL - 56
SP - 1545
EP - 1551
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
IS - 6
ER -