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. / Graduation date: 1994
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/35600 |
| Date | 31 August 1993 |
| Creators | Liu, Qing, 1961- |
| Contributors | Pierce, Donald A. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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