Term of Award

Spring 2024

Degree Name

Master of Science in Mathematics (M.S.)

Document Type and Release Option

Thesis (open access)

Copyright Statement / License for Reuse

Digital Commons@Georgia Southern License

Department

Department of Mathematical Sciences

Committee Chair

Dr. Divine Wanduku

Committee Member 1

Dr. Charles Champ

Committee Member 2

Dr. Shijun Zheng

Abstract

In this thesis, the Weighted Newton-Raphson Method (WNRM), an innovative optimization technique, is introduced in statistical supervised learning for categorization and applied to a diabetes predictive model, to find maximum likelihood estimates. The iterative optimization method solves nonlinear systems of equations with singular Jacobian matrices and is a modification of the ordinary Newton-Raphson algorithm. The quadratic convergence of the WNRM, and high efficiency for optimizing nonlinear likelihood functions, whenever singularity in the Jacobians occur allow for an easy inclusion to classical categorization and generalized linear models such as the Logistic Regression model in supervised learning. The WNRM is thoroughly investigated in the logistic regression model for both repeated and non-repeated response variables. Furthermore, the method is applied to obtain the best-fitted predictive logistic regression model for diabetes health status that depends on several predictor factors for the patients surveyed in a real-life study.

OCLC Number

1437797755

Research Data and Supplementary Material

No

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