Mixed linear models are a time honored method of analyzing correlated data. However, there is still no method of calculating exact confidence intervals or p-values for an arbitrary parameter in any mixed linear model. Instead, researchers must use either specialized approximate and exact tests that have been developed for particular models or rely on likelihood based approximate tests and confidence intervals which may be unreliable in problems with small sample sizes. This thesis develops procedures to improve small sample likelihood based inference in these important models. The first manuscript develops I.M. Skovgaard's modified directed likelihood for mixed linear models and shows how it is a general, accurate, and easy to apply method of improving inference in mixed linear models. In the second manuscript, O.E. Barndorff-Nielsen's approximate modified profile likelihood is applied to mixed linear models. This modified profile likelihood is a sensible generalization of the commonly used residual likelihood and can be applied if either a fixed or a covariance parameter is of interest. The final manuscript discusses how the design of a mixed linear model effects the accuracy of Skovgaard's modified likelihood and suggests a useful decomposition of that statistic. / Graduation date: 1998
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/33989 |
| Date | 14 October 1997 |
| Creators | Lyons, Benjamin |
| Contributors | Peters, Dawn |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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