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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Agyeman, Edwina"],"institution":null,"degree_name":"Master of Science - Mathematical Sciences","degree_level":"Thesis","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":["Dr. Jacob Turner","Dr. Robert Henderson","Dr. Sarah Stovall"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-08-01T07:00:00Z","date_published":"2025-08-01T07:00:00Z","updated_at":"2026-07-24T04:30:49Z","subjects":["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"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.sfasu.edu/etds/628","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Jacob Turner","Dr. Robert Henderson","Dr. Sarah Stovall"]},{"key":"dc:creator","label":"Author","values":["Agyeman, Edwina"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2025-08-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science - Mathematical Sciences"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["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"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.sfasu.edu/etds/628"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["PERFORMANCE OF THE TWO SAMPLE LIKELIHOOD RATIO TEST UNDER A NESTED DIRICHLET: A SIMULATION STUDY"]}]}],"canonical_facts":{"dc:contributor":["Dr. Jacob Turner","Dr. Robert Henderson","Dr. Sarah Stovall"],"dc:creator":["Agyeman, Edwina"],"dc:date.available":["2025-08-07T07:00:00Z"],"dc:description.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.
"],"dc:identifier":["https://scholarworks.sfasu.edu/etds/628"],"dc:subject":["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"],"dc:title":["PERFORMANCE OF THE TWO SAMPLE LIKELIHOOD RATIO TEST UNDER A NESTED DIRICHLET: A SIMULATION STUDY"],"thesis:degree_discipline":["Mathematics and Statistics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science - Mathematical Sciences"]},"updated_at":"2026-07-24T04:30:49Z"}