PERFORMANCE OF THE TWO SAMPLE LIKELIHOOD RATIO TEST UNDER A NESTED DIRICHLET: A SIMULATION STUDY

<p>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.</p>

Name thesis:degree_name

Master of Science - Mathematical Sciences

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Mathematics and Statistics

Year dc:date.available

2025

Author dc:creator

• Agyeman, Edwina

Contributors dc:contributor

• Dr. Jacob Turner
• Dr. Robert Henderson
• Dr. Sarah Stovall

• Dirichlet Distribution
• Nested Dirichlet Distribution
• precision
• Type I error rate
• Mean Vector
• Ternary plot
• Applied Statistics
• Multivariate Analysis
• Other Statistics and Probability
• Probability
• Statistical Methodology
• Statistical Models
• Statistical Theory

Repository record dc:identifier

https://scholarworks.sfasu.edu/etds/628

OAI identifier oai:identifier

oai:scholarworks.sfasu.edu:etds-1689