Date of Award
Summer 8-2025
Degree Type
Thesis
Degree Name
Master of Science - Mathematical Sciences
Department
Mathematics and Statistics
First Advisor
Dr. Jacob Turner
Second Advisor
Dr. Robert Henderson
Third Advisor
Dr. Sarah Stovall
Fourth Advisor
Dr. Billy Harris
Abstract
Compositional data analysis (CoDA) addresses multivariate data constrained to a constant sum, such as proportions or percentages. Originating from early warnings regarding misinterpretation by Pearson (1897), the field was formalized by John Aitchison in 1986, whose foundational work remains highly influential. Over time, new modeling techniques and visualization tools have advanced the field, as noted by Greenacre et al. More recently, Turner et al. proposed an approach based on the Nested Dirichlet Distribution (NDD), which accommodates more flexible dependence structures than the standard Dirichlet model. This thesis builds on the methodology of Turner et al. Chapter 1 introduces the nature of compositional data and explains the limitations of traditional multivariate techniques. Chapter 2 outlines the Dirichlet and Nested Dirichlet models and the associated likelihood ratio test (LRT) framework. Chapter 3 presents a simulation study to evaluate the Type I error performance of the LRT under varying sample sizes, mean vectors, and precision parameters, providing insight into its robustness and applicability.
Repository Citation
Agyeman, Edwina, "PERFORMANCE OF THE TWO SAMPLE LIKELIHOOD RATIO TEST UNDER A NESTED DIRICHLET: A SIMULATION STUDY" (2025). Electronic Theses and Dissertations. 628.
https://scholarworks.sfasu.edu/etds/628
Creative Commons License
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Included in
Applied Statistics Commons, Multivariate Analysis Commons, Other Statistics and Probability Commons, Probability Commons, Statistical Methodology Commons, Statistical Models Commons, Statistical Theory Commons
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