This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.
In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.
Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.
Longitudinal data involving multiple subjects is quite popular in medical and social science areas. I consider generalized linear mixed models (GLMMs) applied to such longitudinal data, and the optimal design searching problem under such models. In this case, based on optimal design theory, the optimality criteria depend on the estimated…
Longitudinal data involving multiple subjects is quite popular in medical and social science areas. I consider generalized linear mixed models (GLMMs) applied to such longitudinal data, and the optimal design searching problem under such models. In this case, based on optimal design theory, the optimality criteria depend on the estimated parameters, which leads to local optimality. Moreover, the information matrix under a GLMM doesn't have a closed-form expression. My dissertation includes three topics related to this design problem. The first part is searching for locally optimal designs under GLMMs with longitudinal data. I apply penalized quasi-likelihood (PQL) method to approximate the information matrix and compare several approximations to show the superiority of PQL over other approximations. Under different local parameters and design restrictions, locally D- and A- optimal designs are constructed based on the approximation. An interesting finding is that locally optimal designs sometimes apply different designs to different subjects. Finally, the robustness of these locally optimal designs is discussed. In the second part, an unknown observational covariate is added to the previous model. With an unknown observational variable in the experiment, expected optimality criteria are considered. Under different assumptions of the unknown variable and parameter settings, locally optimal designs are constructed and discussed. In the last part, Bayesian optimal designs are considered under logistic mixed models. Considering different priors of the local parameters, Bayesian optimal designs are generated. Bayesian design under such a model is usually expensive in time. The running time in this dissertation is optimized to an acceptable amount with accurate results. I also discuss the robustness of these Bayesian optimal designs, which is the motivation of applying such an approach.
