Modeling the random effects covariance matrix for generalized linear mixed models
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. Howeve...
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| Published in | Computational statistics & data analysis Vol. 56; no. 6; pp. 1545 - 1551 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.06.2012
Elsevier |
| Series | Computational Statistics & Data Analysis |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-9473 1872-7352 |
| DOI | 10.1016/j.csda.2011.09.011 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Lee, Keunbaik Hagan, Joseph Yoo, Jae Keun Lee, JungBok |
| Author_xml | – sequence: 1 givenname: Keunbaik surname: Lee fullname: Lee, Keunbaik organization: Department of Statistics, Sungkyunkwan University, Seoul, 110-745, Republic of Korea – sequence: 2 givenname: JungBok surname: Lee fullname: Lee, JungBok organization: Department of Clinical Epidemiology and Biostatistics, Ulsan College of Medicine, Asan Medical Center, 138-736, Republic of Korea – sequence: 3 givenname: Joseph surname: Hagan fullname: Hagan, Joseph organization: Biostatistics Program, School of Public Health, Louisiana State University Health Sciences Center, New Orleans, LA 70112, USA – sequence: 4 givenname: Jae Keun surname: Yoo fullname: Yoo, Jae Keun email: peter.yoo@ewha.ac.kr organization: Department of Statistics, Ewha Womans University, Seoul, Republic of Korea |
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| Cites_doi | 10.1002/sim.1470 10.1093/biomet/88.4.973 10.1002/sim.3352 10.1080/01621459.1993.10594284 10.1093/biomet/89.3.553 10.1093/biomet/86.3.677 10.1111/j.0006-341X.2002.00225.x 10.1002/sim.3534 10.1001/jama.287.3.356 10.1016/j.csda.2006.05.003 10.1080/02664763.2010.515675 10.1016/j.jmva.2009.04.015 10.1093/biomet/90.1.239 10.1093/biomet/87.2.425 10.1111/j.0006-341X.1999.00688.x 10.1191/1471082X06st105oa 10.1017/S0962492900002804 10.1016/j.csda.2010.07.005 |
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| SubjectTerms | Cholesky decomposition Cholesky decomposition Longitudinal data Heterogeneity Covariance matrix Data processing Decomposition Estimates Estimators Heterogeneity Longitudinal data Mathematical models Statistics |
| Title | Modeling the random effects covariance matrix for generalized linear mixed models |
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