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. 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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gonzalez, Jorge & Tuerlinckx, Francis & De Boeck, Paul & Cools, Ronald, 2006. "Numerical integration in logistic-normal models," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1535-1548, December.
- Michael J. Daniels, 2002. "Bayesian analysis of covariance matrices and dynamic models for longitudinal data," Biometrika, Biometrika Trust, vol. 89(3), pages 553-566, August.
- Keunbaik Lee & Sanggil Kang & Xuefeng Liu & Daekwan Seo, 2011. "Likelihood-based approach for analysis of longitudinal nominal data using marginalized random effects models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1577-1590, July.
- Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
- Jianxin Pan, 2003. "On modelling mean-covariance structures in longitudinal studies," Biometrika, Biometrika Trust, vol. 90(1), pages 239-244, March.
- M. Pourahmadi & M. J. Daniels, 2002. "Dynamic Conditionally Linear Mixed Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 58(1), pages 225-231, 03.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1545-1551. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.