This dissertation develops, applies, and investigates new methods to improve the analysis of logistic regression mixture models. An interesting dose-response experiment was previously carried out on a mixed population, in which the class membership of only a subset of subjects (survivors) were subsequently labeled. In early analyses of the dataset, challenges with separation of points and asymmetric confidence intervals were encountered. This dissertation extends the previous analyses by characterizing the model in terms of a mixture of penalized (Firth) logistic regressions and developing methods for constructing profile likelihood-based confidence and inverse intervals, and confidence bands in the context of such a model. The proposed methods are applied to the motivating dataset and another related dataset, resulting in improved inference on model parameters. Additionally, a simulation experiment is carried out to further illustrate the benefits of the proposed methods and to begin to explore better designs for future studies. The penalized model is shown to be less biased than the traditional model and profile likelihood-based intervals are shown to have better coverage probability than Wald-type intervals. Some limitations, extensions, and alternatives to the proposed methods are discussed.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-5742 |
| Date | 01 May 2016 |
| Creators | Flake, Darl D., II |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact Andrew Wesolek (andrew.wesolek@usu.edu). |
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