Ogden, Helen E. (2014) Inference for generalised linear mixed models with sparse structure. PhD thesis, University of Warwick.

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Abstract

The likelihood for the parameters of a generalised linear mixed model involves an
integral which may be of very high dimension. Because of this apparent intractability,
many alternative methods have been proposed for inference in these models, but
it is shown that all can fail when the model is sparse, in that there is only a small
amount of information available on each random effect.
The sequential reduction method developed in this thesis seeks to fill in this
gap, by exploiting the dependence structure of the posterior distribution of the
random effects to reduce dramatically the cost of approximating the likelihood in
models with sparse structure. Examples are given to demonstrate the high quality
of the new approximation relative to the available alternatives.
Finally, robustness of various estimators to misspecification of the random
effect distribution is considered. It is found that certain marginal composite likelihood
estimators are not robust to such misspecification in situations in which the
full maximum likelihood estimator is robust, providing a counterexample to the notion
that composite likelihood estimators will always be at least as robust as the
maximum likelihood estimator under model misspecification.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Linear models (Statistics), Estimation theory, Integrals
Official Date:	February 2014
Dates:	Date Event February 2014 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Firth, D. (David)
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	ix, 105 leaves.
Language:	eng

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