Date of Award:

5-2024

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Mathematics and Statistics

Committee Chair(s)

Stephen J. Walsh

Committee

Stephen J. Walsh

Committee

Brennan Bean

Committee

Daniel Coster

Abstract

The majority of research in the field of optimal design of experiments has focused on producing designs for fixed effects models. The purpose of this thesis is to explore how the optimal design framework applies to nested random effects models. The object that is being optimized is the model information matrix. We explore the full derivation of the random effects information matrix to highlight the complexity of the problem and show how the optimization is a function of the model's parameters. In conjunction with this research, the ODVC (Optimal Design for Variance Components) package was built to provide tools that allow researchers to explore interesting optimal design problems for both one-way and two-way nested random effects models. The tools within this package were used to explore how the choice of an optimal design for a random effects model is influenced by the values of the hypothesized variance components, the sample sizes, and the choice of optimality criteria.

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8ba3995e86c21b07cf60de4424850eb2

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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