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2013 Identifiability of linear mixed effects models
Wei Wang
Electron. J. Statist. 7: 244-263 (2013). DOI: 10.1214/13-EJS770


In linear mixed effects models, the covariance matrix of the response is modeled as the sum of two matrices: the product of the covariance matrix of the random effects with the associated design matrix, and the covariance matrix of the residual error. Building a linear mixed model usually involves selection of the parametrized covariance matrix structures for the random effects and the residual error. However, even if the covariance matrix of the response is not over-parametrized, some specifications of covariance structures can result in the non-identifiability of parameters. When fitting such models, software may or may not indicate a problem with model identifiability. Consequently, it is useful to have a way to check if a model is identifiable which does not rely on the software output. We derive conditions for identifiability of the covariance parameters of the response and study commonly used covariance structures. The derived conditions only rely on the covariance structures being used and properties of the design matrix associated with the random effects and are easy to check.


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Wei Wang. "Identifiability of linear mixed effects models." Electron. J. Statist. 7 244 - 263, 2013.


Received: 1 October 2012; Published: 2013
First available in Project Euclid: 24 January 2013

zbMATH: 1337.62182
MathSciNet: MR3020420
Digital Object Identifier: 10.1214/13-EJS770

Primary: 60K35

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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