Laplace approximations to likelihood functions for generalized linear mixed models Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/b8515r59n

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  • This thesis considers likelihood inferences for generalized linear models with additional random effects. The likelihood function involved ordinarily cannot be evaluated in closed form and numerical integration is needed. The theme of the thesis is a closed-form approximation based on Laplace's method. We first consider a special yet important case of the above general setting -- the Mantel-Haenszel-type model with overdispersion. It is seen that the Laplace approximation is very accurate for likelihood inferences in that setting. The approach and results on accuracy apply directly to the more general setting involving multiple parameters and covariates. Attention is then given to how to maximize out nuisance parameters to obtain the profile likelihood function for parameters of interest. In evaluating the accuracy of the Laplace approximation, we utilized Gauss-Hermite quadrature. Although this is commonly used, it was found that in practice inadequate thought has been given to the implementation. A systematic method is proposed for transforming the variable of integration to ensure that the Gauss-Hermite quadrature is effective. We found that under this approach the Laplace approximation is a special case of the Gauss-Hermite quadrature.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2012-12-11T17:12:16Z (GMT) No. of bitstreams: 1 LiuQing1994.pdf: 2413591 bytes, checksum: 614db65302810dede3823afec53963f3 (MD5)
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2012-12-11T17:11:01Z (GMT) No. of bitstreams: 1 LiuQing1994.pdf: 2413591 bytes, checksum: 614db65302810dede3823afec53963f3 (MD5)

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