Description
In the presence of correlation, generalized linear models cannot be employed to obtain regression parameter estimates. To appropriately address the extravariation due to correlation, methods to estimate and model the additional variation are investigated. A general form of the mean-variance relationship is proposed which incorporates the canonical parameter. The two variance parameters are estimated using generalized method of moments, negating the need for a distributional assumption. The mean-variance relation estimates are applied to clustered data and implemented in an adjusted generalized quasi-likelihood approach through an adjustment to the covariance matrix. In the presence of significant correlation in hierarchical structured data, the adjusted generalized quasi-likelihood model shows improved performance for random effect estimates. In addition, submodels to address deviation in skewness and kurtosis are provided to jointly model the mean, variance, skewness, and kurtosis. The additional models identify covariates influencing the third and fourth moments. A cutoff to trim the data is provided which improves parameter estimation and model fit. For each topic, findings are demonstrated through comprehensive simulation studies and numerical examples. Examples evaluated include data on children’s morbidity in the Philippines, adolescent health from the National Longitudinal Study of Adolescent to Adult Health, as well as proteomic assays for breast cancer screening.
Details
Title
- Essays on the identification and modeling of variance
Contributors
- Irimata, Katherine E (Author)
- Wilson, Jeffrey R (Thesis advisor)
- Kamarianakis, Ioannis (Committee member)
- Kao, Ming-Hung (Committee member)
- Reiser, Mark R. (Committee member)
- Stufken, John (Committee member)
- Arizona State University (Publisher)
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2018
Subjects
Resource Type
Collections this item is in
Note
- thesisPartial requirement for: Ph.D., Arizona State University, 2018
- bibliographyIncludes bibliographical references (pages 68-72)
- Field of study: Statistics
Citation and reuse
Statement of Responsibility
by Katherine E. Irimata